Theorems · Theorem · measure theory

MeasureTheory.Measure.IsEverywherePos.of_forall_exists_nhds_eq

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : MeasurableSpace α] {μ ν : MeasureTheory.Measure α} {s : Set α},
  μ.IsEverywherePos s → (∀ x ∈ s, ∃ t ∈ nhds x, ∀ u ⊆ t, ν u = μ u) → ν.IsEverywherePos s

If two measures coincide locally, then a set which is everywhere positive for the former is also everywhere positive for the latter.

Defined in

Mathlib.MeasureTheory.Measure.EverywherePos

Cited by

3 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasurableSpace