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Fill Lebesgue positivity/empty and Dirac finite additivity - #694

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Chessing234:feat/lebesgue-dirac-fam
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Fill Lebesgue positivity/empty and Dirac finite additivity#694
Chessing234 wants to merge 1 commit into
teorth:mainfrom
Chessing234:feat/lebesgue-dirac-fam

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@Chessing234

@Chessing234 Chessing234 commented Sep 7, 2026

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Summary

  • Lebesgue measure as a finitely additive measure is outer measure, which is nonnegative and vanishes on the empty set.
  • Dirac additivity is a case split on which of two disjoint sets contains the atom.

Test plan

  • lake build Analysis.MeasureTheory.Section_1_4_3; CI covers the module.

Lebesgue measure is outer measure, which is nonnegative and vanishes on empty; Dirac additivity is a case split on which summand contains the atom.
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