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Fill scalar multiplication of finitely additive measures - #700
Chessing234 wants to merge 2 commits into
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Thanks — the content here is good, and I've merged 29 of the sibling PRs from this batch (#686–#718). This one now needs a rebase onto The conflict is purely positional, not substantive: a sibling PR filled other fields of the same structure literal, and git can't line up the context. Concretely, one side of the conflict has the fields that sibling filled (with your field still I resolved all four of the conflicting PRs that way locally and ran a full One suggestion for future batches, since this cost four PRs a round-trip: when several PRs fill different fields of the same structure literal, they will always conflict with each other even though each is individually mergeable against |
Nonnegativity and empty come from EReal; additivity is left-distributivity of the ENNReal coercion.
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rebased onto main. kept each field that already had a proof, and the one this pr fills. |
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Fill finite additivity of scalar multiples of finitely additive measures. Use nonnegativity on measurable sets to apply
EReal.left_distrib_of_nonneg; unrestricted extended-real distributivity is unavailable. The scalar nonnegativity proof also uses the explicit ENNReal coercion lemma.Validation: an isolated Lean check with the actual structure and scalar-multiplication declaration fails for the previous proof (missing
CanonicallyOrderedAdd ERealandLeftDistribClass EReal) and passes for the corrected proof.Full chapter validation is blocked by existing errors in Sections 1.4.1–1.4.3. PR #711 repairs Sections 1.4.1 and 1.4.2, but Section 1.4.3 still fails. The default root currently omits Section 1.4.3, so the ordinary CI check does not validate this change. Keeping this draft until the shared chapter builds.