Theorems · Theorem · measure theory

MeasureTheory.setAverage_sub_setAverage

∀ {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} [CompleteSpace E],
  μ s ≠ ⊤ → ∀ (f : α → E), ∫ (x : α) in s, f x - ⨍ (a : α) in s, f a ∂μ ∂μ = 0

Defined in

Mathlib.MeasureTheory.Integral.Average

Cited by

0 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpace