Theorems · Theorem · probability
ProbabilityTheory.bernoulliMeasure_real_apply_of_mem_of_mem
∀ {X : Type u_1} [inst : MeasurableSpace X] {x y : X} (p : ↑unitInterval) {s : Set X},
MeasurableSet s → x ∈ s → y ∈ s → (ProbabilityTheory.bernoulliMeasure x y p).real s = 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- Set.Elemstatement and proof · cited by 7,166
- MeasurableSetstatement and proof · cited by 3,075
- NNReal.toRealproof · cited by 1,260
- unitIntervalstatement and proof · cited by 607
- MeasureTheory.Measure.realstatement · cited by 530
- unitInterval.symmproof · cited by 69
- unitInterval.toNNRealproof · cited by 34
- ProbabilityTheory.bernoulliMeasurestatement · cited by 19
- ProbabilityTheory.bernoulliMeasure_real_applyproof · cited by 4
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