Theorems · Theorem · probability
ProbabilityTheory.bernoulliMeasure_def
∀ {X : Type u_1} [inst : MeasurableSpace X] (x y : X) (p : ↑unitInterval),
ProbabilityTheory.bernoulliMeasure x y p =
unitInterval.toNNReal p • MeasureTheory.Measure.dirac x +
unitInterval.toNNReal (unitInterval.symm p) • MeasureTheory.Measure.dirac y- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.Elemstatement and proof · cited by 7,166
- NNRealstatement · cited by 4,310
- unitIntervalstatement and proof · cited by 607
- MeasureTheory.Measure.diracstatement · cited by 210
- unitInterval.symmstatement · cited by 69
- unitInterval.toNNRealstatement · cited by 34
- ProbabilityTheory.bernoulliMeasurestatement · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.integral_bernoulliMeasureproof · cited by 0