feat(MeasureTheory): prove elementary and Jordan product measures - #665
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Chessing234 wants to merge 7 commits into
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feat(MeasureTheory): prove elementary and Jordan product measures#665Chessing234 wants to merge 7 commits into
Chessing234 wants to merge 7 commits into
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Exercise 1.1.4: a product of elementary sets is elementary, and elementary measure multiplies. The box-product identities (sides, toSet, injectivity, volume, pairwise disjointness) are the same partition argument already used for disjoint unions.
Exercise 1.1.16: the product of Jordan measurable sets is Jordan measurable, and the measure multiplies. Inner/outer sandwich by elementary products, using Exercise 1.1.4.
CI failed on WithLp convert goals, mem_iUnion witnesses, and missing DecidableEq for Box. Rewrite membership via Fin.ext and iUnion₂.
CI still failed on Fin-index rewrites, nat-add commutation in prod_equiv, and underdetermined Finset.image. Use trans/congr for coordinates and pass explicit Finset.image arguments.
Unfold Box.prod on Nat indices instead of rewriting Fin equalities, and use mem_iUnion₂ the same way the translation proof does.
apply Fin.ext was aimed at the Fin index, but the goal was an equality of sides.
…th the measures min ε 1 is too coarse: (μ+δ)² can overshoot ε when the measures are large. Scale δ by 1/(μ₁+μ₂+1) instead, and rewrite the coordinate squares with rw.
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Summary
Test plan
lake buildlocally (disk is full; the Lean toolchain extract fails). CI is the compiler check.Made with Cursor