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generalize {mfun _ >-> _} #662

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affeldt-aist opened this issue May 25, 2022 · 1 comment · May be fixed by #1256
Open

generalize {mfun _ >-> _} #662

affeldt-aist opened this issue May 25, 2022 · 1 comment · May be fixed by #1256
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wish 🙏 Request for a specific mathematical result

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@affeldt-aist
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analysis/theories/lebesgue_integral.v

Line 68 in bfa6d4b

HB.mixin Record IsMeasurableFun (aT : measurableType) (rT : realType) (f : aT -> rT) := {

while preserving the ring structure of simple functions @CohenCyril
@affeldt-aist affeldt-aist added the wish 🙏 Request for a specific mathematical result label May 25, 2022
@affeldt-aist affeldt-aist mentioned this issue Jul 1, 2022
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@hoheinzollern
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This restriction is preventing a general definition of composition of measurable functions. Here is a restricted definition that works for defining composition of random variables with real-valued functions, used in proving Chernoff's bound.

Lemma measurableT_comp_subproof d1 (T1 : measurableType d1) (f : {mfun R >-> R}) (g : {mfun T1 >-> R}) :
  measurable_fun setT (f \o g).
Proof. apply: measurableT_comp. exact. apply: @measurable_funP _ _ _ g. Qed.

HB.instance Definition _ (d1 : measure_display) (T1 : measurableType d1)
  (f : {mfun R >-> R}) (g : {mfun T1 >-> R}) := isMeasurableFun.Build _ _ _ (f \o g) (@measurableT_comp_subproof _ _ _ _).

@affeldt-aist affeldt-aist linked a pull request Jul 5, 2024 that will close this issue
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Trying to generalize mfun, updated hoheinzollern/analysis
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@hoheinzollern @affeldt-aist