Semiring of Sets

• Autorzy: Roland Coghetto
• Języki publikacji: EN

Abstrakty

EN

Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] 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 Patriota [20] has defined this quasi-semiring. We propose the formalization of some properties developed by the authors.

Słowa kluczowe

EN

sets; set partitions; distributive lattice

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2014
• Tom: 22
• Numer: 1
• Strony: 79-84

Twórcy

autor

Roland Coghetto

• Rue de la Brasserie 5 7100 La Louvière, Belgium

Bibliografia

• [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• [2] Grzegorz Bancerek. Cardinal arithmetics. Formalized Mathematics, 1(3):543-547, 1990.
• [3] Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.
• [4] Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563-567, 1990.
• [5] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
• [6] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• [7] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
• [8] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
• [9] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [10] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [11] Marek Chmur. The lattice of natural numbers and the sublattice of it. The set of prime numbers. Formalized Mathematics, 2(4):453-459, 1991.
• [12] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
• [13] Marek Dudzicz. Representation theorem for finite distributive lattices. Formalized Mathematics, 9(2):261-264, 2001.
• [14] Mariusz Giero. Hierarchies and classifications of sets. Formalized Mathematics, 9(4): 865-869, 2001.
• [15] D.F. Goguadze. About the notion of semiring of sets. Mathematical Notes, 74:346-351, 2003. ISSN 0001-4346. doi:10.1023/A:1026102701631.[Crossref]
• [16] Zbigniew Karno. On discrete and almost discrete topological spaces. Formalized Mathematics, 3(2):305-310, 1992.
• [17] Shunichi Kobayashi and Kui Jia. A theory of partitions. Part I. Formalized Mathematics, 7(2):243-247, 1998.
• [18] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.
• [19] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
• [20] A. G Patriota. A note on Carathéodory’s extension theorem. ArXiv e-prints, 2011.
• [21] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.
• [22] Jean Schmets. Théorie de la mesure. Notes de cours, Université de Liège, 146 pages, 2004.
• [23] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
• [24] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1 (1):187-190, 1990.
• [25] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
• [26] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [27] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
• [28] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

Identyfikatory

DOI

10.2478/forma-2014-0008