Theorems · Theorem · measure theory
MeasureTheory.integral_comp_mul_right_Ioi
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (g : ℝ → E) (a : ℝ) {b : ℝ},
0 < b → ∫ (x : ℝ) in Set.Ioi a, g (x * b) = b⁻¹ • ∫ (x : ℝ) in Set.Ioi (a * b), g x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- mul_commproof · cited by 2,262
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Set.Ioistatement and proof · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- MeasureTheory.integral_comp_mul_left_Ioiproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_comp_mul_right_Ioi'proof · cited by 0