feat(Probability/Distance): add total variation distance tvDist

[allenhaozhu]

Add MeasureTheory.tvDist : Measure α → Measure α → ℝ≥0∞, the total variation distance between two measures, defined via the truncated subtraction μ - ν already in Mathlib.MeasureTheory.Measure.Sub. Add four basic lemmas (tvDist_self, tvDist_comm, tvDist_nonneg, tvDist_le_one) and a bridge lemma tvDist_eq_signedMeasure_totalVariation connecting tvDist to the existing MeasureTheory.SignedMeasure.totalVariation for finite measures.

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AI-assistance disclosure

Per the Mathlib AI-use policy:

• Tool. Claude Code (Anthropic) with the Claude Sonnet 4.6 model.
• Use. I specified the target lemma statements and the proof strategy; the assistant drafted Lean 4 tactic combinations against current Mathlib. I iterated on the proofs, verified each lemma builds under lake build from a clean checkout, and read the final code.
• Vouching. I have read every declaration in this file and can defend the proofs without further AI assistance. I welcome reviewer feedback on naming, namespace placement, and stylistic alignment with the surrounding Mathlib modules.

[github-actions]

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[github-actions]

PR summary 43a9b846af

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Probability.Distance.TotalVariation (new file)	2325

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Declarations diff

+ tvDist
+ tvDist_comm
+ tvDist_eq_signedMeasure_totalVariation
+ tvDist_le_one
+ tvDist_nonneg
+ tvDist_self

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

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No changes to strong technical debt.

No changes to weak technical debt.

[grunweg]

Hello from the triage team! Can you format your PR description according to mathlib's standards (as described here), please?