Theorems · Theorem · measure theory

MeasureTheory.laverage_mem_openSegment_compl_self

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {f : α → ENNReal}
  [MeasureTheory.IsFiniteMeasure μ],
  MeasureTheory.NullMeasurableSet s μ →
    μ s ≠ 0 → μ sᶜ ≠ 0 → ⨍⁻ (x : α), f x ∂μ ∈ openSegment ENNReal (⨍⁻ (x : α) in s, f x ∂μ) (⨍⁻ (x : α) in sᶜ, f x ∂μ)

Defined in

Mathlib.MeasureTheory.Integral.Average

Cited by

0 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsFiniteMeasure