Theorems · Theorem · measure theory
MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℝ → E},
MeasureTheory.Integrable f MeasureTheory.volume → HasSum (fun n => ∫ (x : ℝ) in 0..1, f (x + ↑n)) (∫ (x : ℝ), f x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- zero_addproof · cited by 2,366
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- MeasureTheory.integralstatement and proof · cited by 1,779
- add_commproof · cited by 1,535
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- intervalIntegralstatement and proof · cited by 546
- HasSumstatement and proof · cited by 518
- intervalIntegral.integral_comp_add_rightproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Real.fourierCoeff_tsum_comp_addproof · cited by 1