Commit 2026-02-10 17:28 e0118614

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feat(MeasureTheory.VectorMeasure): add a definition of total variation for VectorMeasure (#26156) This PR adds variation for any VectorMeasure using a supremum definition. Currently mathlib has TotalVariation defined for a signed measure using the Hahn-Jordan decomposition, but this doesn't generalise. Motivation: generally this is an important concept but specifically as a step for proving RMK in the complex case which in turn is a step to prove the spectral theorem. This PR was migrated from #25442. PR divided into smaller pieces, this is just the definition without additional lemmas. PRs adding further results related to variation are:

  • #26160
  • #26165
  • #26168 (shows that for SignedMeasures the two definitions of variation coincide)

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