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Theorems · Theorem · measure theory

MeasureTheory.dirac_eq_dirac_iff

∀ {α : Type u_1} [inst : MeasurableSpace α] [MeasurableSpace.SeparatesPoints α] {x y : α},
  MeasureTheory.Measure.dirac x = MeasureTheory.Measure.dirac y ↔ x = y

Dirac delta measures at two points are equal if and only if the two points are equal, assuming the measurable space separates points.

Defined in
Mathlib.MeasureTheory.Measure.Dirac
Cited by
1 results in Mathlib
Foundations
Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceMeasurableSpace.SeparatesPoints
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Around this declaration

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MeasureTheory.injective_dirac · cited by 0MeasureTheory.injective_d…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Measure.dirac · cited by 210Measure.diracnot_iff_not · cited by 159not_iff_notMeasurableSpace.SeparatesPoints · cited by 18MeasurableSpace.Separates…MeasureTheory.dirac_ne_dirac_iff · cited by 1MeasureTheory.dirac_ne_di…MeasureTheory.dirac_eq_dirac_…CITED BYCITES

Cites6

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Cited by1

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