Theorems · Theorem · measure theory

VitaliFamily.FineSubfamilyOn.measure_le_tsum_of_absolutelyContinuous

∀ {X : Type u_1} [inst : PseudoMetricSpace X] {m0 : MeasurableSpace X} {μ : MeasureTheory.Measure X}
  {v : VitaliFamily μ} {f : X → Set (Set X)} {s : Set X} (h : v.FineSubfamilyOn f s) [SecondCountableTopology X]
  {ρ : MeasureTheory.Measure X}, ρ.AbsolutelyContinuous μ → ρ s ≤ ∑' (p : ↑h.index), ρ (h.covering ↑p)

Defined in

Mathlib.MeasureTheory.Covering.VitaliFamily

Cited by

2 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceSecondCountableTopology