Theorems · Theorem · measure theory

MeasureTheory.setAverage_const

∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  {μ : MeasureTheory.Measure α} [CompleteSpace E] {s : Set α}, μ s ≠ 0 → μ s ≠ ⊤ → ∀ (c : E), ⨍ (x : α) in s, c ∂μ = c

Defined in

Mathlib.MeasureTheory.Integral.Average

Cited by

1 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpace