Theorems · Definition · measure theory
MeasureTheory.ProbabilityMeasure.toFiniteMeasure
{Ω : Type u_1} → [inst : MeasurableSpace Ω] → MeasureTheory.ProbabilityMeasure Ω → MeasureTheory.FiniteMeasure ΩA probability measure can be interpreted as a finite measure.
- 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.FiniteMeasurestatement · cited by 150
- MeasureTheory.ProbabilityMeasurestatement and proof · cited by 127
- MeasureTheory.ProbabilityMeasure.toMeasureproof · cited by 78
Cited by27
Results whose statement or proof uses this declaration.
- MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasureproof · cited by 8
- MeasureTheory.ProbabilityMeasure.mass_toFiniteMeasurestatement · cited by 5
- MeasureTheory.ProbabilityMeasure.apply_monoproof · cited by 5
- MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFnstatement · cited by 4
- MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhdsstatement · cited by 4
- MeasureTheory.ProbabilityMeasure.toWeakDualBCNNproof · cited by 3
- isCompact_setOfPred_probabilityMeasure_mass_eq_compl_isCompact_leproof · cited by 2
- MeasureTheory.FiniteMeasure.testAgainstNN_eq_mass_mulstatement and proof · cited by 2
- MeasureTheory.ProbabilityMeasure.toFiniteMeasure_continuousstatement · cited by 2
- MeasureTheory.ProbabilityMeasure.toFiniteMeasure_isEmbeddingstatement and proof · cited by 2
- MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalizestatement and proof · cited by 2