Theorems · Theorem · measure theory

MeasureTheory.setAverage_congr_fun

∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  {μ : MeasureTheory.Measure α} {s : Set α} {f g : α → E},
  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.Average

Cited by

0 results in Mathlib

Foundations

Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace