Theorems · Definition · probability
ProbabilityTheory.uniformOn
{Ω : Type u_1} → [inst : MeasurableSpace Ω] → Set Ω → MeasureTheory.Measure ΩGiven a set s, uniformOn s is the uniform measure on s, defined as the counting measure
conditioned by s. One should think of uniformOn s t as the proportion of s that is contained
in t.
This is a probability measure when s is finite and nonempty and is given by
ProbabilityTheory.uniformOn_isProbabilityMeasure.
- Defined in
- Mathlib.Probability.UniformOn
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 194 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.
Cites5
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- MeasureTheory.Measure.countproof · cited by 60
- ProbabilityTheory.condproof · cited by 43
Cited by27
Results whose statement or proof uses this declaration.
- ProbabilityTheory.isProbabilityMeasure_uniformOnstatement · cited by 2
- ProbabilityTheory.uniformOn_empty_measstatement · cited by 2
- ProbabilityTheory.uniformOn_selfstatement · cited by 2
- ProbabilityTheory.uniformOn_apply_finsetstatement · cited by 1
- ProbabilityTheory.uniformOn_apply_finset'statement · cited by 1
- ProbabilityTheory.uniformOn_disjoint_unionstatement and proof · cited by 1
- ProbabilityTheory.uniformOn_eq_one_ofstatement and proof · cited by 1
- ProbabilityTheory.uniformOn_eq_zero_iffstatement · cited by 1
- ProbabilityTheory.uniformOn_interstatement and proof · cited by 1
- ProbabilityTheory.uniformOn_inter_selfstatement · cited by 1
- ProbabilityTheory.uniformOn_unionstatement · cited by 1
- ProbabilityTheory.finite_of_uniformOn_ne_zerostatement and proof · cited by 1