Theorems · Theorem · probability

ProbabilityTheory.IndepFun.symm

∀ {Ω : Type u_1} {β : Type u_6} {β' : Type u_7} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {f : Ω → β}
  {g : Ω → β'} {x : MeasurableSpace β} {x_1 : MeasurableSpace β'},
  ProbabilityTheory.IndepFun f g μ → ProbabilityTheory.IndepFun g f μ

Defined in: Mathlib.Probability.Independence.Basic
Cited by: 6 results in Mathlib
Foundations: Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ProbabilityTheory.IndepFunstatement and proof · cited by 192
ProbabilityTheory.Kernel.IndepFun.symmproof · cited by 14

Cited by6

Results whose statement or proof uses this declaration.

ProbabilityTheory.iIndepFun.charFunDual_map_finsetSum_eq_prodproof · cited by 4
ProbabilityTheory.iIndepFun.mgf_sum₀proof · cited by 3
ProbabilityTheory.IndepFun.integrable_right_of_integrable_opproof · cited by 2
ProbabilityTheory.HasSubgaussianMGF.measureReal_le_le_expproof · cited by 0
ProbabilityTheory.iIndepFun.integrable_exp_mul_sumproof · cited by 0
ProbabilityTheory.lintegral_prod_eq_prod_lintegral_of_indepFunproof · cited by 0