Theorems · Theorem · measure theory

MeasureTheory.setIntegral_congr_ae

∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  {f g : X → E} {s : Set X} {μ : MeasureTheory.Measure X},
  MeasurableSet s → (∀ᵐ (x : X) ∂μ, x ∈ s → f x = g x) → ∫ (x : X) in s, f x ∂μ = ∫ (x : X) in s, g x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Set

Cited by

22 results in Mathlib

Foundations

Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace