2016/08/08 by Žikica Perović, Zikica Perovic, Perovic, Zikica +3
Computer Science · Mathematics · #03E10 (secondary) #28Axx #28Bxx (primary) #Advanced Algebra and Logic #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:03E10 #msc:28Axx #msc:28Bxx
paper · pdf · doi:10.48550/arxiv.1608.02468
23 pages
openalex publication_date 2016/08/08 · arxiv created 2016/08/09 · arxiv updated 2016/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Solving a well-known problem of Maharam, Talagrand [17] constructed an exhaustive non uniformly exhaustive submeasure, thus also providing the first example of a Maharam algebra that is not a measure algebra. To each exhaustive submeasure one can canonically assign a certain countable ordinal, its exhaustivity rank. In this paper, we use carefully constructed Schreier families and norms derived from them to provide examples of exhaustive submeasures of arbitrary high exhaustivity rank. This gives rise to uncountably many non isomorphic separable atomless Maharam algebras.