Theorems · Theorem · measure theory

intervalIntegral.integral_comp_mul_add

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b c : ℝ} (f : ℝ → E),
  c ≠ 0 → ∀ (d : ℝ), ∫ (x : ℝ) in a..b, f (c * x + d) = c⁻¹ • ∫ (x : ℝ) in c * a + d..c * b + d, f x

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

4 results in Mathlib

Foundations

Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace