Theorems · Theorem · probability

ProbabilityTheory.iIndepSet.iIndepFun_indicator

∀ {Ω : Type u_1} {ι : Type u_2} {β : Type u_6} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} [inst : Zero β]
  [inst_1 : One β] {m : MeasurableSpace β} {s : ι → Set Ω},
  ProbabilityTheory.iIndepSet s μ → ProbabilityTheory.iIndepFun (fun n => (s n).indicator fun _ω => 1) μ

Defined in: Mathlib.Probability.Independence.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Zero One

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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 and proof · cited by 10,939
Set.indicatorstatement · cited by 723
ProbabilityTheory.iIndepFunstatement · cited by 138
ProbabilityTheory.iIndepSetstatement and proof · cited by 19
ProbabilityTheory.Kernel.iIndepSet.iIndepFun_indicatorproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eqproof · cited by 1