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Theorems · Theorem · probability

PMF.map_apply

∀ {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) (b : β),
  (PMF.map f p) b = ∑' (a : α), if b = f a then p a else 0
Defined in
Mathlib.Probability.ProbabilityMassFunction.Constructions
Cited by
2 results in Mathlib
Foundations
Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

PMF.binomial_one_eq_bernoulli · cited by 0PMF.binomial_one_eq_berno…PMF.map_ofFintype · cited by 0PMF.map_ofFintypeDFunLike.coe · cited by 62936DFunLike.coeENNReal · cited by 9879ENNRealmul_one · cited by 3885mul_oneMulZeroClass.mul_zero · cited by 2091MulZeroClass.mul_zeroSummationFilter.unconditional · cited by 2068SummationFilter.unconditi…tsum · cited by 1148tsummul_ite · cited by 159mul_itePMF · cited by 127PMFPMF.map · cited by 16PMF.mapPMF.map_applyCITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.