Theorems · Theorem · harmonic analysis
Real.tendsto_integral_exp_smul_cocompact
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] (f : ℝ → E),
Filter.Tendsto (fun w => ∫ (v : ℝ), Real.fourierChar (-(v * w)) • f v) (Filter.cocompact ℝ) (nhds 0)The Riemann-Lebesgue lemma for functions on ℝ.
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- Foundations
- Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- mul_commproof · cited by 2,262
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- AddCharstatement · cited by 286
- Circlestatement · cited by 227
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