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fixes #1659 #1660

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Merged
affeldt-aist merged 1 commit into from
Jun 28, 2025
Merged

fixes #1659 #1660

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8 changes: 5 additions & 3 deletions theories/probability.v
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Original file line number Diff line number Diff line change
Expand Up @@ -32,7 +32,9 @@ From mathcomp Require Import ftc gauss_integral hoelder.
(* 'E_P[X] == expectation of the real measurable function X *)
(* covariance X Y == covariance between real random variable X and Y *)
(* 'V_P[X] == variance of the real random variable X *)
(* 'M_ X == moment generating function of the random variable X *)
(* 'M_P X == moment generating function of the random variable X *)
(* with sample space corresponding to the probability *)
(* measure P *)
(* {dmfun T >-> R} == type of discrete real-valued measurable functions *)
(* {dRV P >-> R} == real-valued discrete random variable *)
(* dRV_dom X == domain of the discrete random variable X *)
Expand Down Expand Up @@ -72,7 +74,7 @@ Reserved Notation "'{' 'RV' P >-> R '}'"
(at level 0, format "'{' 'RV' P '>->' R '}'").
Reserved Notation "''E_' P [ X ]" (format "''E_' P [ X ]").
Reserved Notation "''V_' P [ X ]" (format "''V_' P [ X ]").
Reserved Notation "'M_ X t" (at level 5, t, X at level 4, format "''M_' X t").
Reserved Notation "'M_ P X" (at level 5, P, X at level 4, format "''M_' P X").
Reserved Notation "{ 'dmfun' aT >-> T }" (format "{ 'dmfun' aT >-> T }").
Reserved Notation "'{' 'dRV' P >-> R '}'" (format "'{' 'dRV' P '>->' R '}'").

Expand Down Expand Up @@ -619,7 +621,7 @@ Notation "'V_ P [ X ]" := (variance P X).

Definition mmt_gen_fun d (T : measurableType d) (R : realType)
(P : probability T R) (X : T -> R) (t : R) := ('E_P[expR \o t \o* X])%E.
Notation "'M_ X t" := (mmt_gen_fun X t).
Notation "'M_ P X" := (@mmt_gen_fun _ _ _ P X).

Section markov_chebyshev_cantelli.
Local Open Scope ereal_scope.
Expand Down