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[Merged by Bors] - feat: IndepFun.symm of different domains #9425

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[Merged by Bors] - feat: IndepFun.symm of different domains #9425

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3b3496a
feat: `IndepFun.symm` of different domains
llllvvuu Jan 4, 2024
e250556
fixup! feat: `IndepFun.symm` of different domains
llllvvuu Jan 4, 2024
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7 changes: 4 additions & 3 deletions Mathlib/Probability/Independence/Basic.lean
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Expand Up @@ -650,11 +650,12 @@ theorem indepFun_iff_map_prod_eq_prod_map_map {mβ : MeasurableSpace β} {mβ' :
rw [(h₀ hs ht).1, (h₀ hs ht).2, h, Measure.prod_prod]

@[symm]
nonrec theorem IndepFun.symm {_ : MeasurableSpace β} {f g : Ω → β} (hfg : IndepFun f g μ) :
IndepFun g f μ := hfg.symm
nonrec theorem IndepFun.symm {_ : MeasurableSpace β} {_ : MeasurableSpace β'}
(hfg : IndepFun f g μ) : IndepFun g f μ := hfg.symm
#align probability_theory.indep_fun.symm ProbabilityTheory.IndepFun.symm

theorem IndepFun.ae_eq {mβ : MeasurableSpace β} {f g f' g' : Ω → β} (hfg : IndepFun f g μ)
theorem IndepFun.ae_eq {mβ : MeasurableSpace β} {mβ' : MeasurableSpace β'}
{f' : Ω → β} {g' : Ω → β'} (hfg : IndepFun f g μ)
(hf : f =ᵐ[μ] f') (hg : g =ᵐ[μ] g') : IndepFun f' g' μ := by
refine kernel.IndepFun.ae_eq hfg ?_ ?_ <;>
simp only [ae_dirac_eq, Filter.eventually_pure, kernel.const_apply]
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7 changes: 4 additions & 3 deletions Mathlib/Probability/Independence/Kernel.lean
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Expand Up @@ -788,10 +788,11 @@ theorem indepFun_iff_indepSet_preimage {mβ : MeasurableSpace β} {mβ' : Measur
· rwa [← indepSet_iff_measure_inter_eq_mul (hf hs) (hg ht) κ μ]

@[symm]
nonrec theorem IndepFun.symm {_ : MeasurableSpace β} {f g : Ω → β} (hfg : IndepFun f g κ μ) :
IndepFun g f κ μ := hfg.symm
nonrec theorem IndepFun.symm {_ : MeasurableSpace β} {_ : MeasurableSpace β'}
(hfg : IndepFun f g κ μ) : IndepFun g f κ μ := hfg.symm

theorem IndepFun.ae_eq {mβ : MeasurableSpace β} {f g f' g' : Ω → β} (hfg : IndepFun f g κ μ)
theorem IndepFun.ae_eq {mβ : MeasurableSpace β} {mβ' : MeasurableSpace β'}
{f' : Ω → β} {g' : Ω → β'} (hfg : IndepFun f g κ μ)
(hf : ∀ᵐ a ∂μ, f =ᵐ[κ a] f') (hg : ∀ᵐ a ∂μ, g =ᵐ[κ a] g') :
IndepFun f' g' κ μ := by
rintro _ _ ⟨A, hA, rfl⟩ ⟨B, hB, rfl⟩
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