Theorems · Theorem · measure theory

MeasurableSet.exists_isClosed_sdiff_lt

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace α]
  [OpensMeasurableSpace α] [μ.WeaklyRegular] ⦃A : Set α⦄,
  MeasurableSet A → μ A ≠ ⊤ → ∀ {ε : ENNReal}, ε ≠ 0 → ∃ F ⊆ A, IsClosed F ∧ μ (A \ F) < ε

Defined in

Mathlib.MeasureTheory.Measure.Regular

Cited by

3 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceOpensMeasurableSpaceMeasureTheory.Measure.WeaklyRegular