Theorems · Theorem · measure theory

VitaliFamily.eventually_measure_lt_top

∀ {α : Type u_1} [inst : PseudoMetricSpace α] {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  (v : VitaliFamily μ) [MeasureTheory.IsLocallyFiniteMeasure μ] (x : α), ∀ᶠ (a : Set α) in v.filterAt x, μ a < ⊤

For every point x, sufficiently small sets in a Vitali family around x have finite measure. (This is a trivial result, following from the fact that the measure is locally finite).

Defined in

Mathlib.MeasureTheory.Covering.Differentiation

Cited by

4 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceMeasureTheory.IsLocallyFiniteMeasure