Theorems · Theorem · measure theory

MeasureTheory.setLIntegral_congr_fun_ae

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal} {s : Set α},
  MeasurableSet s → (∀ᵐ (x : α) ∂μ, x ∈ s → f x = g x) → ∫⁻ (x : α) in s, f x ∂μ = ∫⁻ (x : α) in s, g x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Basic

Cited by

11 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound