[Merged by Bors] - feat: f i * f j, f k * f l are independent if f is
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Also prove that a subsingleton family is always independent and that an independent family imples the measure is a probability measure. This latter result means we can drop `IsProbabilityMeasure μ` assumptions from many theorems.
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| variable {m : ∀ i, MeasurableSpace (κ i)} {f : ∀ i, Ω → κ i} | ||
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| @[nontriviality] | ||
| lemma iIndepFun.of_subsingleton [IsProbabilityMeasure μ] [Subsingleton ι] : iIndepFun m f μ := |
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Out of scope, but: this should be IIndepFun, right?
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Maybe, unclear. Might be better as IndepFuns
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Dec 20, 2023
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Also prove that a subsingleton family is always independent and that an independent family implies the measure is a probability measure. This latter result means we can drop `IsProbabilityMeasure μ` assumptions from many theorems. From PFR Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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f i * f j, f k * f l are independent if f isf i * f j, f k * f l are independent if f is
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Also prove that a subsingleton family is always independent and that an independent family implies the measure is a probability measure.
This latter result means we can drop
IsProbabilityMeasure μassumptions from many theorems.From PFR