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Fill sigma-algebra order, infima, and the Mathlib union bridge - #692

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Chessing234:feat/sigma-algebra-order
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Fill sigma-algebra order, infima, and the Mathlib union bridge#692
Chessing234 wants to merge 1 commit into
teorth:mainfrom
Chessing234:feat/sigma-algebra-order

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@Chessing234

@Chessing234 Chessing234 commented Sep 7, 2026

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Summary

  • The inclusion order on concrete sigma-algebras is the same pointwise order as on boolean algebras: reflexivity, transitivity, antisymmetry, top, and bot.
  • Infima are pointwise; countable union of bot is empty or univ according as every summand is empty.
  • Finite union in Mathlib's MeasurableSpace is a two-term countable union, which fills the remaining field of sigmaAlgebra.

Test plan

  • lake build Analysis.MeasureTheory.Section_1_4_2; CI covers the module.

The order is the same pointwise inclusion as the boolean-algebra instance; finite union in MeasurableSpace is a two-term countable union.
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