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$(L, M)$ -fuzzy $σ$ -algebras.

Shi, Fu-Gui (2010)

International Journal of Mathematics and Mathematical Sciences

"Paradoxe" Zerlegung Euklidischer Räume.

Walter A. Deuber (1993)

Elemente der Mathematik

$σ$ -porosity is separably determined

Marek Cúth, Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

We prove a separable reduction theorem for $σ$ -porosity of Suslin sets. In particular, if $A$ is a Suslin subset in a Banach space $X$ , then each separable subspace of $X$ can be enlarged to a separable subspace $V$ such that $A$ is $σ$ -porous in $X$ if and only if $A \cap V$ is $σ$ -porous in $V$ . Such a result is proved for several types of $σ$ -porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem...

σ-ideals and related Baire systems

R. Mauldin (1971)

Fundamenta Mathematicae

σ-ring and σ-algebra of Sets1

Noboru Endou, Kazuhisa Nakasho, Yasunari Shidama (2015)

Formalized Mathematics

In this article, semiring and semialgebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semiring of sets has already been formalized in [13], that is, strictly speaking, a definition of a quasi semiring of sets suggested in the last few decades [15]. We adopt a classical definition of a semiring of sets here to avoid such a confusion. Ring of sets and algebra of sets have been formalized as non empty preboolean set [23] and field of subsets [18],...