Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Bernoulli sampling lemma #1240

Draft
wants to merge 4 commits into
base: master
Choose a base branch
from
Draft
Show file tree
Hide file tree
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
77 changes: 77 additions & 0 deletions CHANGELOG_UNRELEASED.md
Original file line number Diff line number Diff line change
Expand Up @@ -15,6 +15,38 @@
- in `lebesgue_measure.v`:
+ lemma `measurable_indicP`

- 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 `mapping_display`, `g_sigma_algebra_mappingType`, `g_sigma_algebra_mapping`,
notations `.-mapping`, `.-mapping.-measurable`

- in `lebesgue_measure.v`:
+ lemmas `measurable_funrpos`, `measurable_funrneg`

- 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 `mapping_display`, `g_sigma_algebra_mappingType`, `g_sigma_algebra_mapping`,
notations `.-mapping`, `.-mapping.-measurable`

- in `lebesgue_measure.v`:
+ lemmas `measurable_funrpos`, `measurable_funrneg`

- in `lebesgue_integral.v`:
+ definition `dyadic_approx` (was `Let A`)
+ definition `integer_approx` (was `Let B`)
Expand All @@ -28,6 +60,42 @@
+ lemma `expectation_def`
+ notation `'M_`

- new file `independence.v`:
+ lemma `expectationM_ge0`
+ definition `independent_events`
+ definition `mutual_independence`
+ definition `independent_RVs`
+ definition `independent_RVs2`
+ lemmas `g_sigma_algebra_mapping_comp`, `g_sigma_algebra_mapping_funrpos`,
`g_sigma_algebra_mapping_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`
- in `lebesgue_integral.v`:
+ lemma `abse_integralP`
- in `signed.v`:
+ definition `onem_NngNum`
- in `measure.v`:
+ definition `bernoulli`, declared as a probability measure instance
- in `itv.v`:
+ canonical `onem_itv01`

- new file `independence.v`:
+ lemma `expectationM_ge0`
+ definition `independent_events`
+ definition `mutual_independence`
+ definition `independent_RVs`
+ definition `independent_RVs2`
+ lemmas `g_sigma_algebra_mapping_comp`, `g_sigma_algebra_mapping_funrpos`,
`g_sigma_algebra_mapping_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`

- in `lebesgue_integral.v`:
+ lemmas `integrable_pushforward`, `integral_pushforward`
+ lemma `integral_measure_add`
Expand Down Expand Up @@ -64,6 +132,7 @@

- in `probability.v`:
+ `integral_distribution` -> `ge0_integral_distribution`
+ `expectationM` -> `expectationMl`

### Generalized

Expand All @@ -89,6 +158,14 @@

### Removed

- in `topology_structure.v`:
+ lemma `closureC`

- in file `lebesgue_integral.v`:
+ lemma `approximation`

### Removed

- 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)
Expand Down
2 changes: 2 additions & 0 deletions _CoqProject
Original file line number Diff line number Diff line change
Expand Up @@ -86,6 +86,8 @@ theories/lebesgue_integral.v
theories/ftc.v
theories/hoelder.v
theories/probability.v
theories/independence.v
theories/sampling.v
theories/convex.v
theories/charge.v
theories/kernel.v
Expand Down
5 changes: 3 additions & 2 deletions reals/itv.v
Original file line number Diff line number Diff line change
Expand Up @@ -850,6 +850,9 @@ Lemma inum_lt : {mono inum : x y / (x < y)%O}. Proof. by []. Qed.

End Morph.

Canonical onem_itv01 {R : realDomainType} (p : {i01 R}) : {i01 R} :=
@Itv.mk _ _ (onem p%:inum) [itv of 1 - p%:inum].

Section Test1.

Variable R : numDomainType.
Expand Down Expand Up @@ -890,8 +893,6 @@ Definition s_of_pq (p q : {i01 R}) : {i01 R} :=
Lemma s_of_p0 (p : {i01 R}) : s_of_pq p 0%:i01 = p.
Proof. by apply/val_inj; rewrite /= subr0 mulr1 subKr. Qed.

Canonical onem_itv01 (p : {i01 R}) : {i01 R} :=
@Itv.mk _ _ (onem p%:inum) [itv of 1 - p%:inum].

Definition s_of_pq' (p q : {i01 R}) : {i01 R} :=
(`1- (`1-(p%:inum) * `1-(q%:inum)))%:i01.
Expand Down
1 change: 1 addition & 0 deletions reals/signed.v
Original file line number Diff line number Diff line change
Expand Up @@ -123,6 +123,7 @@ From mathcomp Require Import mathcomp_extra.
(* Canonical instances are also provided according to types, as a *)
(* fallback when no known operator appears in the expression. Look to *)
(* nat_snum below for an example on how to add your favorite type. *)
(* *)
(******************************************************************************)

Reserved Notation "{ 'compare' x0 & nz & cond }"
Expand Down
2 changes: 2 additions & 0 deletions theories/Make
Original file line number Diff line number Diff line change
Expand Up @@ -52,6 +52,8 @@ lebesgue_integral.v
ftc.v
hoelder.v
probability.v
independence.v
sampling.v
lebesgue_stieltjes_measure.v
convex.v
charge.v
Expand Down
Loading
Loading