Theorems · Theorem · harmonic analysis
UnitAddTorus.integral_preimage
∀ {d : Type u_1} [inst : Fintype d] {E : Type u_3} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E]
(f : UnitAddTorus d → E) (a : d → ℝ),
∫ (x : UnitAddTorus d), f x = ∫ (x : d → ℝ) in {x | ∀ (i : d), x i ∈ Set.Ioc (a i) (a i + 1)}, f fun i => ↑(x i)- Defined in
- Mathlib.Analysis.Fourier.AddCircleMulti
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpaceproof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measureproof · cited by 10,939
- Fintypestatement and proof · cited by 7,736
- Set.Elemproof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
Cited by1
Results whose statement or proof uses this declaration.
- UnitAddTorus.mFourierCoeff_eq_integralproof · cited by 0