expectation of product

CHANGELOG_UNRELEASED.md

@@ -27,12 +27,46 @@
   + lemma `integral0oo_atan`
 
 - in `measure.v`:
-  + lemmas `preimage_set_system0`, `preimage_set_systemU`, `preimage_set_system_comp`
+  + lemmas `preimage_set_system0`, `preimage_set_systemU`, `preimage_set_system_compS`
   + lemma `preimage_set_system_id`
 
 - in `Rstruct_topology.v`:
   + lemma `RexpE`
 
+- file `mathcomp_extra.v`:
+  + lemma `mulr_funEcomp`
+
+- 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`
+  + defintions `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_RVs_comp`, `independent_RVs_scale`,
+    `independent_RVs2_funrposneg`,
+    `independent_RVs2_funrnegpos`, `independent_RVs2_funrnegneg`,
+    `independent_RVs2_funrpospos`
+  + lemma `expectationM_ge0`, `integrable_expectationM`, `independent_integrableM`,
+    ` expectation_mul`
+
 ### Changed
 
 - file `nsatz_realtype.v` moved from `reals` to `reals-stdlib` package
@@ -55,7 +89,7 @@
   + `min_le_min` -> `le_min2`
   + `max_le_max` -> `le_max2`
   + `real_sqrtC` -> `sqrtC_real`
-
+  
 ### Generalized
 
 - in `constructive_ereal.v`:
@@ -74,6 +108,31 @@
   + lemma `deg_le2_ge0` (available as `deg_le2_poly_ge0` in `ssrnum.v`
     since MathComp 2.1.0)
 
+- in `lebesgue_integral.v`:
+  + definition `cst_mfun`
+  + lemma `mfun_cst`
+
+- in `cardinality.v`:
+  + lemma `cst_fimfun_subproof`
+
+- in `lebesgue_integral.v`:
+  + lemma `cst_mfun_subproof` (use lemma `measurable_cst` instead)
+  + lemma `cst_nnfun_subproof` (turned into a `Let`)
+  + lemma `indic_mfun_subproof` (use lemma `measurable_fun_indic` instead)
+
+- in `lebesgue_integral.v`:
+  + lemma `measurable_indic` (was uselessly specializing `measurable_fun_indic` (now `measurable_indic`) from `lebesgue_measure.v`)
+  + notation `measurable_fun_indic` (deprecation since 0.6.3)
+- in `constructive_ereal.v`
+  + notation `lee_opp` (deprecated since 0.6.5)
+  + notation `lte_opp` (deprecated since 0.6.5)
+- in `measure.v`:
+  + `dynkin_setI_bigsetI` (use `big_ind` instead)
+
+- in `lebesgue_measurable.v`:
+  + notation `measurable_fun_power_pos` (deprecated since 0.6.3)
+  + notation `measurable_power_pos` (deprecated since 0.6.4)
+
 ### Infrastructure
 
 ### Misc

_CoqProject

@@ -89,6 +89,7 @@ theories/lebesgue_integral.v
 theories/ftc.v
 theories/hoelder.v
 theories/probability.v
+theories/independence.v
 theories/convex.v
 theories/charge.v
 theories/kernel.v

classical/mathcomp_extra.v

@@ -697,3 +697,7 @@ Proof.
 move=> lt_mn i; rewrite big_nat [ltRHS]big_nat ltr_sum//.
 by apply/hasP; exists m; rewrite ?mem_index_iota leqnn lt_mn.
 Qed.
+
+Lemma mulr_funEcomp (R : semiRingType) (T : Type) (x : R) (f : T -> R) :
+  x \o* f = *%R^~ x \o f.
+Proof. by []. Qed.

theories/Make

@@ -54,6 +54,7 @@ lebesgue_integral.v
 ftc.v
 hoelder.v
 probability.v
+independence.v
 lebesgue_stieltjes_measure.v
 convex.v
 charge.v