Theorems · Theorem · general topology

MeasurableSet.residualEq_isOpen

∀ {α : Type u_1} [inst : TopologicalSpace α] {s : Set α} [inst_1 : MeasurableSpace α] [BorelSpace α],
  MeasurableSet s → ∃ u, IsOpen u ∧ s =ᶠ[residual α] u

Any Borel set differs from some open set by a meager set.

Defined in

Mathlib.Topology.Baire.BaireMeasurable

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasurableSpaceBorelSpace