Theorems · Theorem · measure theory

intervalIntegral.integral_symm

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℝ → E} {μ : MeasureTheory.Measure ℝ}
  (a b : ℝ), ∫ (x : ℝ) in b..a, f x ∂μ = -∫ (x : ℝ) in a..b, f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

35 results in Mathlib

Foundations

Depth 251 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace