Theorems · Theorem · measure theory

MeasureTheory.Measure.sigmaFinite_iff_measure_singleton_lt_top

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [Countable α],
  MeasureTheory.SigmaFinite μ ↔ ∀ (a : α), μ {a} < ⊤

A measure on a countable space is sigma-finite iff it gives finite mass to every singleton. See measure_singleton_lt_top for the forward direction without the countability assumption.

Defined in

Mathlib.MeasureTheory.Measure.Typeclasses.SFinite

Cited by

0 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Countable