Theorems · Theorem · measure theory

MeasureTheory.integral_comp_rpow_Ioi

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (g : ℝ → E) {p : ℝ},
  p ≠ 0 → ∫ (x : ℝ) in Set.Ioi 0, (|p| * x ^ (p - 1)) • g (x ^ p) = ∫ (y : ℝ) in Set.Ioi 0, g y

Substitution y = x ^ p in integrals over Ioi 0

Defined in

Mathlib.MeasureTheory.Integral.IntegralEqImproper

Cited by

3 results in Mathlib

Foundations

Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace