Theorems · Theorem · measure theory
intervalIntegral.integral_comp_add_right
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} (f : ℝ → E) (d : ℝ),
∫ (x : ℝ) in a..b, f (x + d) = ∫ (x : ℝ) in a + d..b + d, f x- Cited by
- 9 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measureproof · cited by 10,939
- MeasureTheory.integralproof · cited by 1,779
- MeasureTheory.Measure.restrictproof · cited by 1,646
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Set.Iocproof · cited by 971
- intervalIntegralstatement and proof · cited by 546
- add_sub_cancel_rightproof · cited by 187
- MeasurableEmbeddingproof · cited by 170
Cited by9
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_comp_mul_addproof · cited by 4
- intervalIntegral.integral_comp_sub_rightproof · cited by 3
- Function.Periodic.intervalIntegral_add_zsmul_eqproof · cited by 2
- intervalIntegral.integral_comp_add_leftproof · cited by 2
- EulerSine.integral_cos_pow_eqproof · cited by 2
- MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_intproof · cited by 1
- bernoulliFun_mulproof · cited by 1
- MonotoneOn.intervalIntegral_slope_leproof · cited by 1
- Real.circleAverage_eq_integral_addproof · cited by 1