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Theorems · Theorem · probability

SimpleGraph.binomialRandom_eq_map

∀ (V : Type u_1) (p : ↑unitInterval) [Countable V],
  SimpleGraph.binomialRandom V p =
    MeasureTheory.Measure.map SimpleGraph.fromEdgeSet (ProbabilityTheory.setBernoulli Sym2.diagSetᶜ p)
Defined in
Mathlib.Probability.Combinatorics.BinomialRandomGraph.Defs
Cited by
2 results in Mathlib
Foundations
Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Countable
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Around this declaration

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

SimpleGraph.binomialRandom_zero · cited by 0SimpleGraph.binomialRando…SimpleGraph.binomialRandom_one · cited by 0SimpleGraph.binomialRando…Set · cited by 53352SetReal · cited by 25697RealMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureSet.Elem · cited by 7166Set.ElemSimpleGraph · cited by 3072SimpleGraphCompl.compl · cited by 2925Compl.complFilter.univ_mem' · cited by 1672Filter.univ_mem'Filter.mp_mem · cited by 1537Filter.mp_memMeasureTheory.Measure.map · cited by 858Measure.mapSym2 · cited by 737Sym2Countable · cited by 633CountableunitInterval · cited by 607unitIntervalSimpleGraph.fromEdgeSet · cited by 43SimpleGraph.fromEdgeSetSym2.diagSet · cited by 41Sym2.diagSetProbabilityTheory.setBernoulli · cited by 19ProbabilityTheory.setBern…SimpleGraph.binomialRandom_eq…CITED BYCITES

Cites22

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Cited by2

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