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Fill Lebesgue outer measure of the empty set and monotonicity - #690

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Chessing234:feat/lebesgue-outer-empty-mono
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Fill Lebesgue outer measure of the empty set and monotonicity#690
Chessing234 wants to merge 1 commit into
teorth:mainfrom
Chessing234:feat/lebesgue-outer-empty-mono

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@Chessing234 Chessing234 commented Sep 7, 2026

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Summary

  • Exercise 1.2.3 (i): the empty set is a countable set, so in positive dimension it has outer measure zero; in dimension 0 the existing characterisation already gives 0.
  • Exercise 1.2.3 (ii): every box cover of F is a cover of E when E ⊆ F, so the infimum of covering volumes is monotone.

Test plan

  • lake build Analysis.MeasureTheory.Section_1_2_1 once mathlib is available; CI covers the module.

These are Exercise 1.2.3 (i) and (ii); empty uses the countable-null lemma, and monotonicity is that every cover of F is a cover of E.
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