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Boolean Valued and Stone Algebra Valued Measure Theories
Author(s) -
Nishimura Hirokazu
Publication year - 1994
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19940400110
Subject(s) - mathematics , measure (data warehouse) , generalization , boolean algebra , algebra over a field , field (mathematics) , subject (documents) , pure mathematics , discrete mathematics , mathematical analysis , computer science , database , library science
In conventional generalization of the main results of classical measure theory to Stone algebra valued measures, the values that measures and functions can take are Booleanized, while the classical notion of a σ‐field is retained. The main purpose of this paper is to show by abundace of illustrations that if we agree to Booleanize the notion of a σ‐field as well, then all the glorious legacy of classical measure theory is preserved completely. Mathematics Subject Classification: 03C90, 28B15.