Theorems · Theorem · measure theory

IsCompact.exists_isOpen_lt_of_lt

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace α]
  [μ.InnerRegularCompactLTTop] [MeasureTheory.IsLocallyFiniteMeasure μ] [R1Space α] [BorelSpace α] {K : Set α},
  IsCompact K → ∀ (r : ENNReal), μ K < r → ∃ U, K ⊆ U ∧ IsOpen U ∧ μ U < r

Defined in

Mathlib.MeasureTheory.Measure.Regular

Cited by

3 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceMeasureTheory.Measure.InnerRegularCompactLTTopMeasureTheory.IsLocallyFiniteMeasureR1SpaceBorelSpace