Theorems · Theorem · measure theory

MeasureTheory.Measure.ext_of_Iic

∀ {α : Type u_5} [inst : TopologicalSpace α] {m : MeasurableSpace α} [SecondCountableTopology α]
  [inst_2 : LinearOrder α] [OrderTopology α] [BorelSpace α] (μ ν : MeasureTheory.Measure α)
  [MeasureTheory.IsFiniteMeasure μ], (∀ (a : α), μ (Set.Iic a) = ν (Set.Iic a)) → μ = ν

Two finite measures on a Borel space are equal if they agree on all left-infinite right-closed intervals.

Defined in

Mathlib.MeasureTheory.Constructions.BorelSpace.Order

Cited by

2 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceSecondCountableTopologyLinearOrderOrderTopologyBorelSpaceMeasureTheory.IsFiniteMeasure