Theorems · Theorem · measure theory

MeasureTheory.isTightMeasureSet_singleton

∀ {α : Type u_3} [inst : MeasurableSpace α] [inst_1 : TopologicalSpace α]
  [TopologicalSpace.IsCompletelyPseudoMetrizableSpace α] [SecondCountableTopology α] [BorelSpace α]
  {μ : MeasureTheory.Measure α} [MeasureTheory.IsFiniteMeasure μ], MeasureTheory.IsTightMeasureSet {μ}

In a complete second-countable pseudo-metric space, finite measures are tight.

Defined in

Mathlib.MeasureTheory.Measure.Tight

Cited by

2 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceTopologicalSpace.IsCompletelyPseudoMetrizableSpaceSecondCountableTopologyBorelSpaceMeasureTheory.IsFiniteMeasure