feat: covarianceBilin of the push-forward measure

[EtienneC30]

---

• depends on: feat: introduce covarianceBilin #30324
• depends on: [Merged by Bors] - refactor: make ContinuousLinearMap.id protected #30362

From BrownianMotion

[github-actions]

PR summary c48ea032ed

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Probability.Moments.CovarianceBilin	2325	2334	+9 (+0.39%)

Import changes for all files

Files	Import difference
Mathlib.Probability.Moments.CovarianceBilin	9

---

Declarations diff

+ covarianceBilin
+ covarianceBilinDual_self_nonneg
+ covarianceBilin_apply
+ covarianceBilin_apply_basisFun
+ covarianceBilin_apply_basisFun_self
+ covarianceBilin_apply_eq_cov
+ covarianceBilin_apply_pi
+ covarianceBilin_comm
+ covarianceBilin_eq_covarianceBilinDual
+ covarianceBilin_map
+ covarianceBilin_map_const_add
+ covarianceBilin_of_not_memLp
+ covarianceBilin_real
+ covarianceBilin_real_self
+ covarianceBilin_self
+ covarianceBilin_self_nonneg
+ covarianceBilin_zero
+ integral_comp_id_comm
+ integral_comp_id_comm'
+ integral_id_map
+ isPosSemidef_covarianceBilin
+ toBilinForm
+ toBilinForm_apply

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• feat: introduce covarianceBilin #30324
• [Merged by Bors] - refactor: make ContinuousLinearMap.id protected #30362
  By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.