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Theorems · Definition · measure theory

MeasureTheory.FiniteMeasure.normalize

{Ω : Type u_1} →
  [Nonempty Ω] → {m0 : MeasurableSpace Ω} → MeasureTheory.FiniteMeasure Ω → MeasureTheory.ProbabilityMeasure Ω

Normalize a finite measure so that it becomes a probability measure, i.e., divide by the total mass.

Defined in
Mathlib.MeasureTheory.Measure.ProbabilityMeasure
Cited by
15 results in Mathlib
Foundations
Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Nonempty

Around this declaration

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

MeasureTheory.FiniteMeasure.testAgainstNN_eq_mass_mul · cited by 2FiniteMeasure.testAgainst…MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero · cited by 2FiniteMeasure.normalize_e…MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize · cited by 2FiniteMeasure.self_eq_mas…MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize · cited by 2FiniteMeasure.self_eq_mas…MeasureTheory.FiniteMeasure.tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass · cited by 1FiniteMeasure.tendsto_of_…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.FiniteMeasure.toMeasure_normalize_eq_of_nonzero · cited by 1FiniteMeasure.toMeasure_n…MeasureTheory.FiniteMeasure.tendsto_normalize_of_tendsto · cited by 1FiniteMeasure.tendsto_nor…MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNN_of_tendsto · cited by 1FiniteMeasure.tendsto_nor…MeasureTheory.FiniteMeasure.average_eq_integral_normalize · cited by 0FiniteMeasure.average_eq_…MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero · cited by 0FiniteMeasure.normalize_e…MeasureTheory.FiniteMeasure.normalize.congr_simp · cited by 0normalize.congr_simpProbabilityMeasure.toFiniteMeasure_normalize_eq_self · cited by 0ProbabilityMeasure.toFini…MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto · cited by 0FiniteMeasure.tendsto_nor…MeasurableSpace · cited by 13106MeasurableSpaceNonempty.some · cited by 340Nonempty.someMeasureTheory.Measure.dirac · cited by 210Measure.diracMeasureTheory.FiniteMeasure · cited by 150MeasureTheory.FiniteMeasu…MeasureTheory.ProbabilityMeasure · cited by 127MeasureTheory.Probability…MeasureTheory.FiniteMeasure.toMeasure · cited by 87FiniteMeasure.toMeasureMeasureTheory.FiniteMeasure.mass · cited by 46FiniteMeasure.massFiniteMeasure.normalizeCITED BYCITES

Cites7

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Cited by15

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