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The Broughton--Huff theorem on increasing unions of sigma-fields

Yi-Jing Tseng

Palomar Registrypalomar/PALOMAR-2026-09-12-000001Sep 12, 2026math.PRscore 0

A Lean formalization of the Broughton--Huff theorem that the ordinary union of a strictly increasing sequence of sigma-fields is not a sigma-field. The proof also proves the existence of a set measurable in the lattice supremum but in none of the individual sigma-fields.

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