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Finitely-additive, countably-additive and internal probability measures

Haosui Duanmu, William Weiss (2018)

Commentationes Mathematicae Universitatis Carolinae

We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is infinitesimal. As an application to standard probability theory, we show that every finitely-additive Borel probability measure P on a separable metric space is a limit of a sequence of countably-additive Borel probability measures { P n } n ∈ ℕ in the sense that ∫ f d P = lim n → ∞ ∫ f d P n for all bounded...

Finiteness and choice

Omar De la Cruz (2002)

Fundamenta Mathematicae

We deal with weak choice principles of the form: Every "finite" family of non-empty sets has a choice function, where "finite" stands for one of several different definitions of finiteness that are not equivalent unless we assume the axiom of choice (AC). Several relations of implication and independence are established. In the process, we answer a few open questions about the relations between different definitions of finiteness.

Finite-to-one fuzzy maps and fuzzy perfect maps

Francisco Gallego Lupiañez (1998)

Kybernetika

In this paper we define, for fuzzy topology, notions corresponding to finite-to-one and k -to-one maps. We study the relationship between these new fuzzy maps and various kinds of fuzzy perfect maps. Also, we show the invariance and the inverse inveriance under the various kinds of fuzzy perfect maps (and the finite-to-one fuzzy maps), of different properties of fuzzy topological spaces.

First Order Languages: Further Syntax and Semantics

Marco Caminati (2011)

Formalized Mathematics

Third of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are introduced....

Fixed points of fuzzy monotone maps

Ismat Beg (1999)

Archivum Mathematicum

The existence of fixed points for monotone maps on the fuzzy ordered sets under suitable conditions is proved.

Fixed points theorems of non-expanding fuzzy multifunctions

Abdelkader Stouti (2005)

Archivum Mathematicum

We prove the existence of a fixed point of non-expanding fuzzy multifunctions in α -fuzzy preordered sets. Furthermore, we establish the existence of least and minimal fixed points of non-expanding fuzzy multifunctions in α -fuzzy ordered sets.

Fixed points with respect to the L-slice homomorphism σ a

K.S. Sabna, N.R. Mangalambal (2019)

Archivum Mathematicum

Given a locale L and a join semilattice J with bottom element 0 J , a new concept ( σ , J ) called L -slice is defined,where σ is as an action of the locale L on the join semilattice J . The L -slice ( σ , J ) adopts topological properties of the locale L through the action σ . It is shown that for each a ∈ L , σ a is an interior operator on ( σ , J ) .The collection M = { σ a ; a ∈ L } is a Priestly space and a subslice of L - Hom ( J , J ) . If the locale L is spatial we establish an isomorphism between the L -slices ( σ , L ) and ( δ , M ) . We have shown that the fixed set of σ a ,...

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