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Theorems · Theorem · measure theory

MeasureTheory.measureReal_le_one

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.IsZeroOrProbabilityMeasure μ]
  {s : Set α}, μ.real s ≤ 1
Defined in
Mathlib.MeasureTheory.Measure.Typeclasses.Probability
Cited by
1 results in Mathlib
Foundations
Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.IsZeroOrProbabilityMeasure
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.tendstoInDistribution_of_tendstoInMeasure_sub · cited by 2MeasureTheory.tendstoInDi…Set · cited by 53352SetReal · cited by 25697RealMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Measure.real · cited by 530Measure.realzero_le_one · cited by 316zero_le_oneENNReal.ofReal_one · cited by 61ENNReal.ofReal_oneMeasureTheory.IsZeroOrProbabilityMeasure · cited by 46MeasureTheory.IsZeroOrPro…ENNReal.toReal_le_of_le_ofReal · cited by 14ENNReal.toReal_le_of_le_o…MeasureTheory.prob_le_one · cited by 11MeasureTheory.prob_le_oneMeasureTheory.measureReal_le_…CITED BYCITES

Cites10

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

Cited by1

Results whose statement or proof uses this declaration.