Prove2Me

`BookProof.ChapterPaleyWienerSampling.BandLimited.integrable_fourier` (hf : BandLimited T f) : Integrable (๐“• f)

Proved
BookProof.ChapterPaleyWienerSampling.BandLimited.integrable_fourier

by leonardopedro ยท Oct 20, 2026 ยท Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPaleyWienerSampling.

BookProof.ChapterPaleyWienerSampling.BandLimited.integrable_fourier (hf : BandLimited T f) : Integrable (๐“• f)

Formalization note: Lean 4 identifier BookProof.ChapterPaleyWienerSampling.BandLimited.integrable_fourier.

Preamble
-- Generated from ChapterPaleyWienerSampling.lean โ€” theorem BookProof.ChapterPaleyWienerSampling.BandLimited.integrable_fourier
import Definitions.Def_ChapterShannonSampling
import Mathlib
import Definitions.Def_ChapterPaleyWienerSampling
open BookProof.ChapterPaleyWienerSampling
open BookProof.ChapterPaleyWienerSampling



open MeasureTheory Complex AddCircle Set
open scoped Real FourierTransform
open BookProof.ChapterShannonSampling (sinc bandSignal exists_rep half_add_period)

variable {T : โ„} {f g : โ„ โ†’ โ„‚}
Formal statement
theorem BookProof.ChapterPaleyWienerSampling.BandLimited.integrable_fourier (hf : BandLimited T f) : Integrable (๐“• f) := by sorry

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