Fill Lebesgue positivity/empty and Dirac finite additivity

[Chessing234]

Fill nonnegativity and the empty-set value for Lebesgue measure, and finite additivity for Dirac measure by splitting on membership of the atom. Remove the obsolete Set.not_mem_empty reference in the existing Dirac empty-set proof.

Validation: isolated Lean checks of these declarations pass using the actual finitely additive measure structure.

Full chapter validation is blocked by existing errors in Section 1.4.3, including its scalar-action instances. PR #711 repairs the prerequisite Boolean and sigma-algebra chapters. The default root omits Section 1.4.3, so ordinary CI does not validate these declarations. Keeping this draft until the shared chapter builds.

[teorth]

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 main before it can go in.

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 sorry), and the other side has your field filled (with theirs still sorry). The resolution is just the union — take whichever side has the real proof for each field, discarding the sorry version.

I resolved all four of the conflicting PRs that way locally and ran a full lake build: 8310 jobs, no errors. So this is mechanical, and nothing about your proof needs to change.

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 main. Grouping the fields of one structure into a single PR avoids it entirely — and would be easier to review, too.

[Chessing234]

rebased onto main. kept each field that already had a proof, and the one this pr fills.