Theorems · Theorem · measure theory

MeasurableSet.exists_isOpen_diff_lt

Deprecated since 2026-06-03Use MeasurableSet.exists_isOpen_sdiff_lt instead.

∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace α] [μ.OuterRegular]
  {A : Set α}, MeasurableSet A → μ A ≠ ⊤ → ∀ {ε : ENNReal}, ε ≠ 0 → ∃ U ⊇ A, IsOpen U ∧ μ U < ⊤ ∧ μ (U \ A) < ε

Alias of MeasurableSet.exists_isOpen_sdiff_lt.

Defined in

Mathlib.MeasureTheory.Measure.Regular

Cited by

0 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceMeasureTheory.Measure.OuterRegular