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Theorems · Definition · measure theory

MeasureTheory.ProbabilityMeasure.toFiniteMeasure

{Ω : Type u_1} → [inst : MeasurableSpace Ω] → MeasureTheory.ProbabilityMeasure Ω → MeasureTheory.FiniteMeasure Ω

A probability measure can be interpreted as a finite measure.

Defined in
Mathlib.MeasureTheory.Measure.ProbabilityMeasure
Cited by
26 results in Mathlib
Foundations
Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace

Around this declaration

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

MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure · cited by 8ProbabilityMeasure.ennrea…MeasureTheory.ProbabilityMeasure.mass_toFiniteMeasure · cited by 5ProbabilityMeasure.mass_t…MeasureTheory.ProbabilityMeasure.apply_mono · cited by 5ProbabilityMeasure.apply_…MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn · cited by 4ProbabilityMeasure.coeFn_…MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds · cited by 4ProbabilityMeasure.tendst…MeasureTheory.ProbabilityMeasure.toWeakDualBCNN · cited by 3ProbabilityMeasure.toWeak…isCompact_setOfPred_probabilityMeasure_mass_eq_compl_isCompact_le · cited by 2isCompact_setOfPred_proba…MeasureTheory.FiniteMeasure.testAgainstNN_eq_mass_mul · cited by 2FiniteMeasure.testAgainst…MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto · cited by 2ProbabilityMeasure.tendst…MeasureTheory.ProbabilityMeasure.toFiniteMeasure_continuous · cited by 2ProbabilityMeasure.toFini…MeasureTheory.ProbabilityMeasure.toFiniteMeasure_isEmbedding · cited by 2ProbabilityMeasure.toFini…MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize · cited by 2FiniteMeasure.self_eq_mas…MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass · cited by 1FiniteMeasure.tendsto_tes…MeasureTheory.FiniteMeasure.normalize_testAgainstNN · cited by 1FiniteMeasure.normalize_t…MeasureTheory.ProbabilityMeasure.toFiniteMeasure_nonzero · cited by 1ProbabilityMeasure.toFini…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.FiniteMeasure · cited by 150MeasureTheory.FiniteMeasu…MeasureTheory.ProbabilityMeasure · cited by 127MeasureTheory.Probability…MeasureTheory.ProbabilityMeasure.toMeasure · cited by 78ProbabilityMeasure.toMeas…ProbabilityMeasure.toFiniteMe…CITED BYCITES

Cites4

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Cited by27

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