Theorems · Theorem · probability

ProbabilityTheory.setBernoulli_apply

∀ {ι : Type u_1} {u : Set ι} {p : ↑unitInterval} (S : Set (Set ι)),
  (ProbabilityTheory.setBernoulli u p) S =
    (MeasureTheory.Measure.infinitePi fun i =>
        unitInterval.toNNReal p • MeasureTheory.Measure.dirac (i ∈ u) +
          unitInterval.toNNReal (unitInterval.symm p) • MeasureTheory.Measure.dirac False)
      ((fun t i => i ∈ t) '' S)

Defined in

Mathlib.Probability.Distributions.SetBernoulli

Cited by

2 results in Mathlib

Foundations

Depth 280 from the axioms · uses propext, Classical.choice, Quot.sound