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Semiring of sets. (English) Zbl 1298.28002

Summary: J. Schmets [Théorie de la mesure. Notes de cours, Université de Liège (2004)] has developed a measure theory from a generalized notion of a semiring of sets. D. F. Goguadze [Math. Notes 74, No. 3, 346–351 (2003); translation from Mat. Zametki 74, No. 3, 362–368 (2003; Zbl 1072.28001)] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that A. G. Patriota [“A note on Carathéodory’s extension theorem”, Preprint, arXiv:1103.6166] has defined this quasi-semiring. We propose the formalization of some properties developed by the authors.

MSC:

28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
03E02 Partition relations
03B35 Mechanization of proofs and logical operations

Citations:

Zbl 1072.28001
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References:

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