Theorems · Theorem · measure theory

MeasureTheory.Measure.isEverywherePos_iff_of_forall_exists_nhds_eq

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

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

Defined in

Mathlib.MeasureTheory.Measure.EverywherePos

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasurableSpace