expectation of product

CHANGELOG_UNRELEASED.md

@@ -48,6 +48,43 @@
   + lemmas `leq_prime_seq`, `mem_prime_seq`
   + theorem `dvg_sum_inv_prime_seq`
 
+
+- file `mathcomp_extra.v`
+  + lemmas `ge_trunc`, `lt_succ_trunc`, `trunc_ge_nat`, `trunc_lt_nat`
+
+- in `measure.v`:
+  + lemma `preimage_set_system_compS`
+
+- in `numfun.v`:
+  + defintions `funrpos`, `funrneg` with notations `^\+` and `^\-`
+  + lemmas `funrpos_ge0`, `funrneg_ge0`, `funrposN`, `funrnegN`, `ge0_funrposE`,
+    `ge0_funrnegE`, `le0_funrposE`, `le0_funrnegE`, `ge0_funrposM`, `ge0_funrnegM`,
+    `le0_funrposM`, `le0_funrnegM`, `funr_normr`, `funrposneg`, `funrD_Dpos`,
+    `funrD_posD`, `funrpos_le`, `funrneg_le`
+  + lemmas `funerpos`, `funerneg`
+
+- in `measure.v`:
+  + lemma `preimage_class_comp`
+  + definitions `preimage_display`, `g_sigma_algebra_preimageType`, `g_sigma_algebra_preimage`,
+    notations `.-preimage`, `.-preimage.-measurable`
+
+- in `measurable_realfun.v`:
+  + lemmas `measurable_funrpos`, `measurable_funrneg`
+
+- new file `independence.v`:
+  + lemma `expectationM_ge0`
+  + definition `independent_events`
+  + definition `mutual_independence`
+  + definition `independent_RVs`
+  + definition `independent_RVs2`
+  + lemmas `g_sigma_algebra_preimage_comp`, `g_sigma_algebra_preimage_funrpos`,
+    `g_sigma_algebra_preimage_funrneg`
+  + lemmas `independent_RVs2_comp`, `independent_RVs2_funrposneg`,
+    `independent_RVs2_funrnegpos`, `independent_RVs2_funrnegneg`,
+    `independent_RVs2_funrpospos`
+  + lemma `expectationM_ge0`, `integrable_expectationM`, `independent_integrableM`,
+    ` expectation_prod`
+
 ### Changed
 
 - in `lebesgue_stieltjes_measure.v` specialized from `numFieldType` to `realFieldType`:

_CoqProject

@@ -113,6 +113,7 @@ theories/lebesgue_integral_theory/lebesgue_integral.v
 theories/ftc.v
 theories/hoelder.v
 theories/probability.v
+theories/independence.v
 theories/convex.v
 theories/charge.v
 theories/kernel.v

experimental_reals/discrete.v

@@ -4,7 +4,7 @@
 (* Copyright (c) - 2016--2018 - Polytechnique                           *)
 
 (* -------------------------------------------------------------------- *)
-From Corelib Require Setoid.
+From Coq Require Setoid.
 From HB Require Import structures.
 From mathcomp Require Import all_ssreflect all_algebra.
 From mathcomp.classical Require Import boolp.

reals/reals.v

@@ -43,7 +43,7 @@
 (*                                                                            *)
 (******************************************************************************)
 
-From Corelib Require Import Setoid.
+From Coq Require Import Setoid.
 From HB Require Import structures.
 From mathcomp Require Import all_ssreflect all_algebra archimedean.
 From mathcomp Require Import boolp classical_sets set_interval.

theories/Make

@@ -78,6 +78,7 @@ lebesgue_integral_theory/lebesgue_integral.v
 ftc.v
 hoelder.v
 probability.v
+independence.v
 lebesgue_stieltjes_measure.v
 convex.v
 charge.v