Theorems · Theorem · measure theory

MeasureTheory.Measure.OuterRegular.ext_isOpen_isBounded

∀ {α : Type u_3} [inst : PseudoMetricSpace α] {mα : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [μ.OuterRegular]
  [ν.OuterRegular], (∀ (U : Set α), IsOpen U → Bornology.IsBounded U → μ U = ν U) → μ = ν

Outer regular measures are determined by values on bounded open sets.

Defined in: Mathlib.MeasureTheory.Measure.Regular
Cited by: 0 results in Mathlib
Foundations: Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoMetricSpace MeasureTheory.Measure.OuterRegular MeasureTheory.Measure.OuterRegular

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DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Set.iUnionproof · cited by 2,483
iSupproof · cited by 2,415
IsOpenstatement and proof · cited by 2,400
PseudoMetricSpacestatement and proof · cited by 1,550
Monotoneproof · cited by 1,397
Bornology.IsBoundedstatement and proof · cited by 293
MeasureTheory.Measure.OuterRegularstatement and proof · cited by 24

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