Theorems · Definition · measure theory

MeasureTheory.diracProbaHomeomorph

{X : Type u_1} →
  [inst : MeasurableSpace X] →
    [inst_1 : TopologicalSpace X] →
      [inst_2 : OpensMeasurableSpace X] →
        [T0Space X] → [CompletelyRegularSpace X] → X ≃ₜ ↑(Set.range MeasureTheory.diracProba)

In a completely regular T0 topological space X, diracProbaEquiv is a homeomorphism to its image in ProbabilityMeasure X.

Defined in: Mathlib.MeasureTheory.Measure.DiracProba
Cited by: 1 results in Mathlib
Foundations: Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace TopologicalSpace OpensMeasurableSpace T0Space CompletelyRegularSpace

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Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
Set.Elemstatement · cited by 7,166
Set.rangestatement · cited by 4,705
Homeomorphstatement · cited by 725
OpensMeasurableSpacestatement and proof · cited by 636
T0Spacestatement and proof · cited by 179
MeasureTheory.ProbabilityMeasurestatement · cited by 127
CompletelyRegularSpacestatement and proof · cited by 23
MeasureTheory.diracProbastatement · cited by 15
MeasureTheory.diracProbaEquivproof · cited by 5

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.isEmbedding_diracProbaproof · cited by 0