Measure theory 1.2.4: require nonempty sets in dist_of_disj_compact_pos#540
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Measure theory 1.2.4: require nonempty sets in dist_of_disj_compact_pos#540Chessing234 wants to merge 1 commit into
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Empty compact sets make set_dist 0 via sInf of an empty set, contradicting > 0. Co-authored-by: Cursor <cursoragent@cursor.com>
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This was referenced Jun 24, 2026
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Summary
dist_of_disj_compact_posclaimedset_dist E F > 0for any disjoint compact sets, but fails when either set is empty.Root cause
set_dist E F = sInf (dist '' (E ×ˢ F)). ForE = ∅, the image is empty andsInf ∅ = 0, contradicting> 0. Empty sets are compact and disjoint from anything.Fix
Require
E.NonemptyandF.Nonempty.Test plan
lake buildpasses