Theorems · Theorem · measure theory

MeasureTheory.Measure.InnerRegularWRT.of_sigmaFinite

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [MeasureTheory.SigmaFinite μ],
  μ.InnerRegularWRT (fun s => MeasurableSet s ∧ μ s ≠ ⊤) fun s => MeasurableSet s

Given a σ-finite measure, any measurable set can be approximated from inside by a measurable set of finite measure.

Defined in

Mathlib.MeasureTheory.Measure.Regular

Cited by

0 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasureTheory.SigmaFinite