Petitioner was convicted in Florida state court of armed burglary and first-degree murder. A sentence of death was imposed. The Florida Supreme Court affirmed Petitioner’s conviction and sentence and later denied post-conviction relief. Petitioner then filed this petition in federal court seeking a writ of habeas corpus. The District Court denied habeas relief but granted a certificate of appealability on two issues, and this appeal commenced.

Background

Petitioner was convicted in Florida state court for armed burglary and the murder of his neighbor, who before her death had been pursuing charges against Petitioner for the theft of $140 from her car. The Victim was stabbed to death in her home, which showed signs of a break-in. After the Victim was last seen alive and before her body discovered, video recordings showed Petitioner using her ATM card and driving a car similar to hers. Petitioner was also found with checkbooks belonging to the Victim.

While in jail, Petitioner made various inculpatory statements to fellow inmates Mark DaCosta (“DaCosta”) and William Palmer (“Palmer”). DaCosta and Palmer later testified against Petitioner at the Grand Jury hearing resulting in Petitioner’s indictment; Palmer also testified at trial.

Following Petitioner’s conviction for armed burglary and first-degree murder, the trial judge — consistent with the jury’s earlier recommendation — imposed a capital sentence. On direct appeal, the Florida Supreme Court affirmed both Petitioner’s convictions and death sentence. Consalvo v. State, 697 So.2d 805 (Fla.1996) (“Consalvo I”).

Petitioner next challenged his convictions and death sentence by filing a motion for post-conviction relief in state trial court. The state trial court held an evidentiary hearing and considered Petitioner’s many claims for relief, including recent recantations of testimony by several witnesses. The state trial court determined that the witnesses’ recantation testimony was incredible. Instead, the state trial court credited the testimony of the state attorneys, who refuted the testimony[*844] of the recanting witnesses. The state trial court entered a final order denying Petitioner’s amended motion for post-conviction relief. And the Florida Supreme Court affirmed the state trial court’s denial of the post-conviction motion. Consalvo v. State, 937 So.2d 555 (Fla.2006) (“Consalvo II”).

Petitioner next turned to the federal courts for post-conviction relief, filing this habeas petition and raising many claims for relief. The District Court denied Petitioner’s habeas petition and later denied Petitioner’s motion to amend or alter its judgment. But the District Court granted a certificate of appealability on two issues: (1) Whether the state supreme court unreasonably applied federal law in affirming the trial court’s rejection of Petitioner’s constitutional claims under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963) and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972); and (2) Whether the state supreme court unreasonably applied clearly established federal law in rejecting Petitioner’s claim that reference to evidence during sentencing that was not presented in open court was harmful and violated his constitutional rights as promulgated by the Supreme Court in Gardner v. Florida, 430 U.S. 349, 97 S.Ct. 1197, 51 L.Ed.2d 393 (1977).

Standard of Review

Petitioner’s habeas petition is subject to the provisions of the Antiterrorism and Effective Death Penalty Act of 1996, Pub L. 104-132, 110 Stat. 1214 (1996) (codified in scattered sections of Title 28 of the U.S.Code) (“the AEDPA”). To obtain habeas relief under the AEDPA, Petitioner must demonstrate that the state court’s post-conviction ruling was (1) “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States;” or (2) “based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d)(1), (2). The AEDPA imposes an “exacting standard.” Maharaj v. Sec’y, Dep’t of Corr., 432 F.3d 1292, 1308 (11th Cir.2005).

A state court’s decision is “contrary to” federal law if the “state court arrives at a conclusion opposite to that reached by [the Supreme] Court on a question of law or if the state court decides a case differently than [the Supreme] Court has on a set of materially indistinguishable facts.” Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 1523, 146 L.Ed.2d 389 (2000). A state court’s decision is based on an “unreasonable application” of federal law if “the state court identifies the correct governing legal principle from [the Supreme] Court’s decisions but unreasonably applies that principle to the facts of the prisoner’s case.” Id. Findings of fact by a state court are presumed correct, and a petitioner for habeas corpus must rebut the presumption by clear and convincing evidence. See Hunter v. Sec’y, Dep’t of Corr., 395 F.3d 1196, 1200 (11th Cir.2005).

We review de novo the District Court’s decision about whether the state court’s ruling was contrary to federal law, involved an unreasonable application of federal law, or was based on an unreasonable determination of the facts. Smith v. Sec’y, Dep’t of Corr., 572 F.3d 1327, 1332 (11th Cir.2009).

Discussion

A. Petitioner’s Brady and Giglio Claims

Petitioner argues that he is entitled to habeas relief because the state withheld material exculpatory evidence and knowingly presented false or misleading evidence to the jury at his trial. Brady requires the state to disclose material ex[*845] culpatory evidence in its possession. 83 S.Ct. at 1196-97. The duty to disclose required by Brady includes the disclosure of evidence that may be used for impeachment purposes and evidence that may be used to attack the “thoroughness and even the good faith of the investigation[.]” Kyles v. Whitley, 514 U.S. 419, 115 S.Ct. 1555, 1571, 131 L.Ed.2d 490 (1995). Giglio is closely related and dictates that the presentation of known false evidence violates due process and is “incompatible with rudimentary demands of justice.” 92 S.Ct. at 766 (internal quotation marks omitted).

To summarize, Petitioner claims the state did not meet its Brady obligations in failing to disclose these things: the identity of Informant DaCosta; that prosecutors met with and supplied information to Da-Costa; that prosecutors recruited DaCosta to act as the state’s agent; that prosecutors purposefully had DaCosta placed in Petitioner’s pod at a jail; that DaCosta spoke to Informant Palmer about Petitioner’s ease at the state’s behest and provided Palmer with information received from the state; and that Palmer made false statements to detectives, in grand jury testimony, and at trial.

In a similar way, Petitioner claims that, in contravention of Giglio, the state violated his due process rights by failing to correct the false testimony of DaCosta and Palmer and by using the false testimony to the state’s benefit. Petitioner asserts that both DaCosta and Palmer received favorable treatment and leniency from prosecutors in exchange for their cooperation in Petitioner’s case. Petitioner points to Da-Costa and Palmer’s later recantations of their testimony inculpating Petitioner— and the allegedly inconsistent testimony of Assistant State’s Attorney (“ASA”) Ken Farnsworth — at the state court post-conviction evidentiary hearing. Florida points to the state court post-conviction evidentiary hearing testimony of ASA Brian Cavanagh and others, who countered the recantations of DaCosta and Palmer.

Petitioner’s Brady and Giglio claims turn upon credibility: the dispositive determination is whether to credit the state post-conviction hearing recantations of Da-Costa and Palmer or the contradictory testimony of the assistant state’s attorney (among others) at the same hearing.

Determining the credibility of witnesses is the province and function of the state courts, not a federal court engaging in habeas review. Federal habeas courts have “no license to redetermine credibility of witnesses whose demeanor has been observed by the state trial court, but not by them.” Marshall v. Lonberger, 459 U.S. 422, 103 S.Ct. 843, 851, 74 L.Ed.2d 646 (1983). We consider questions about the credibility and demeanor of a witness to be questions of fact. See Freund v. Butterworth, 165 F.3d 839, 862 (11th Cir.1999) (en banc). And the AEDPA affords a presumption of correctness to a factual determination made by a state court; the habeas petitioner has the burden of overcoming the presumption of correctness by clear and convincing evidence. 28 U.S.C. § 2254(e).

At the state post-conviction evidentiary hearing, the state court credited the testimony of the state’s witnesses. The state court credited ASA Cavanagh’s testimony that he never met with DaCosta in jail and never promised DaCosta leniency in exchange for his testimony. Nor did the state court find ASA Farnsworth’s testimony to be inconsistent with that of ASA Cavanagh, as Petitioner suggested it was. The state court in addition found incredible the testimony of DaCosta and Palmer, who recanted their earlier testimony in[*846] criminating Petitioner. ^[1] The state court thus denied relief.

The Florida Supreme Court considered the issue and affirmed the first state court’s denial of post-conviction relief. The Florida Supreme Court reasoned that “competent, substantial evidence” supported the lower state court’s determinations. Consalvo II, 987 So.2d at 562. According to the Florida Supreme Court, “there existed no exculpatory evidence ... that the State should have turned over to the defense----” Id. at 563. As such, the Florida Supreme Court denied the Petitioner’s Brady claim. And because the Florida Supreme Court affirmed the state trial court’s determination that ASA Cavanagh’s post-conviction hearing testimony was credible and not inconsistent with ASA Farnsworth’s testimony, it likewise concluded that no Giglio error existed because “the trial court did not err in concluding that no misleading testimony in fact existed.” Id. Therefore, according to the Florida Supreme Court, no misleading or false testimony had been presented at trial. It also noted that Petitioner’s conviction was supported by other credible evidence. ^[2]

Per section 2254, the District Court examined this issue and found and concluded that “the record does not reveal that the [District Court’s] deference to the state supreme court’s affirmance of the trial court’s decision would be misplaced.” D. Ct. Order at 11. The District Court thus determined that the Petitioner had failed to overcome the presumption of correctness afforded to the state trial court’s finding of fact, and the District Court denied Petitioner’s Brady and Giglio claims.

In affirming the state trial court’s denial of Petitioner’s Brady and Giglio claims, the Florida Supreme Court did not contravene clearly established federal law, unreasonably apply clearly established federal law, or reach an unreasonable determination of the facts.

Petitioner’s Brady claim hangs on the existence of exculpatory evidence, and Petitioner’s Giglio claim hangs on the existence of false or misleading evidence offered at trial. Because the state courts found that DaCosta and Palmer’s recantation testimony was incredible (instead crediting the contradictory testimony presented by the state), no exculpatory evidence was shown by Petitioner to have been withheld; and no false or misleading testimony was shown to have been presented at trial. Petitioner has not carried his AEDPA-imposed burden of establishing that the state court’s factual determination was unreasonable, and therefore Petitioner has also not established that Brady and Giglio were contravened or unreasonably applied by the Florida Supreme Court. We affirm the District Court’s decision to deny relief on these claims.

B. Petitioner’s Gardner Claim

Petitioner contends that the sentencing state court, in its sentencing order,[*847] erred in relying on deposition testimony that was not presented in open court either at the guilt or the penalty phase. Petitioner also contends that this error was not — and cannot be — harmless.

Gardner establishes that a “petitioner [is] denied due process of law when the death sentence [is] imposed, at least in part, on the basis of information which he had no opportunity to deny or explain.” 97 S.Ct. at 1207. In Gardner, the Supreme Court concluded that a criminal defendant was denied due process of law when a capital sentence was imposed partly on the basis of confidential information in a pre-sentence report which had not been disclosed to the defendant.

In contrast to the facts in Gardner, the information the sentencing court cited in this case came from deposition testimony, which was available to all parties. Although the information cited by the sentencing court was available to all parties in advance of the sentencing, the Florida Supreme Court concluded that the trial court erred in referring to the deposition testimony. Consalvo I, 697 So.2d at 818. But the Florida Supreme Court also concluded that, because “the trial court did not actually rely on any information that was not otherwise proven during trial,” any error was “harmless beyond a reasonable doubt and that the error complained of did not contribute to the sentence of death.” Id.

Petitioner contends that the Florida Supreme Court’s decision is objectively unreasonable and that the District Court erred in accepting the state high court’s conclusion. Petitioner additionally contends that no harmless-error standard of review applies in such a case: that reference to deposition testimony at sentencing is a per se due process violation and harmful.

But the Supreme Court has never held that harmless error analysis cannot apply to this kind of error. Instead, Supreme Court precedent instructs reviewing courts generally to engage in a harmless error analysis. See, e.g., Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 827, 17 L.Ed.2d 705 (1967); Brecht v. Abrahamson, 507 U.S. 619, 113 S.Ct. 1710, 1721-22, 123 L.Ed.2d 353 (1993). We accept that the “harmless error” doctrine can be reasonably applied to the kind of error at sentencing that Petitioner advances here.

The Florida Supreme Court applied this harmless error analysis to the sentencing judge’s reference to deposition testimony. Petitioner claims that the sentencing court erred in referencing the deposition testimony of Officer William Hopper, who stated that the Victim was “a little scared of Robert [Consalvo].” Ample trial evidence, however, permits the inference that the Victim was “a little scared” of Petitioner, even without the sentencing court’s reference to Officer Hopper’s deposition testimony.

For instance, Detective Thomas Gill testified that the Victim had her locks changed after a set of her keys disappeared. Another detective, Detective Douglas Doethlaff, testified that the Victim suspected Consalvo in the theft of her money and keys. And the Victim’s brother testified that the Victim said she was feeling “down” because, among other reasons, Consalvo had stolen her money and keys. Consalvo’s mother, in addition, testified that the Victim had spoken to her about her missing money and keys. Based on this — and possibly other — evidence, the sentencing judge could have inferred that the Victim was “a little scared” of Consalvo, even without reference to Officer Hopper’s deposition testimony. We accept that the reference to Officer Hopper’s deposition testimony was reasonably seen by the state courts as a harmless error: the non-trial deposition testimony referenced[*848] facts that were established by other competent evidence at trial.

In addition, Petitioner claims that relief is warranted due to the improper reliance on Detective Doethlaffs deposition testimony by the sentencing court. But a comparison of Detective Doethlaffs deposition testimony with his trial testimony reveals that Doethlaffs trial testimony was consistent with his deposition testimony. Because the complained-of deposition testimony of Detective Doethlaff was essentially the same as the testimony provided by Doethlaff at trial, the error of citing the deposition testimony was reasonably seen by the state courts as harmless beyond a reasonable doubt.

Petitioner finally argues that the sentencing judge improperly referenced testimony from Petitioner’s girlfriend or ex-girlfriend, Gail Russell. The sentencing judge erred in stating that Russell, during the guilt phase of Consalvo’s trial, testified about Consalvo driving the Victim’s car and possessing the Victim’s keys: Russell did not testify at the guilt phase of the trial. But other witnesses, namely motel manager Real Favreau and Detective Gill, did testify at the guilt phase to facts substantially in accord with the complained-of facts that the sentencing court erroneously attributed to Russell. Therefore, the state supreme court reasonably concluded that the mistaken reference to Russell’s supposed trial testimony constituted harmless error because the sentencing court did not actually rely on operative facts that were unevidenced at trial.

Petitioner has not carried his AEDPAimposed burden of demonstrating that the Florida Supreme Court’s conclusion that the sentencer’s reference to non-trial testimony — the substance of which was proved by other evidence at trial — was contrary to or involved an unreasonable application of clearly established Supreme Court precedent. Therefore, Petitioner is entitled to no habeas relief on this claim.

Conclusion

The District Court’s order denying Petitioner’s habeas petition is

AFFIRMED.