Search

In nonstandard poly-saturated model, the properties of Loeb measure generated by finite kernel are studied. Firstly, the corresponding Loeb measure is constructed with the internal finite kernel in internal measurable spaces. Then, the properties of Loeb measures generated by internal finite kernel are discussed in internal measurable spaces and product measurable spaces. Finally, Keisler's Fubini theorem of Loeb measure generated by internal finite kernel is proved in internal product measurable spaces. [ABSTRACT FROM AUTHOR]

The separated properties of topological spaces under enlarged model are studied by using non-standard analysis method, and their characterizations are given. Finally it is proved that product of a class of special compact sets is a compact set in the product reasoning closure spaces. [ABSTRACT FROM AUTHOR]

In this paper, the m-convergence of fuzzy nets in [0.1]-topological spaces is researched in nonstandard enlargement, and the nonstandard characterization of m-convergence is obtained. First, the * -fuzzy sets are defined by transfer principle, and N-monad and Q-monad are proposed. Then, the nonstandard characterizations of N-convergence and Q-convergence of fuzzy nets are shown with the monads, respectively. At last, m-convergence of fuzzy nets is characterized, and the connections between fuzzy Hausdorff and m-convergence are discussed. [ABSTRACT FROM AUTHOR]

The conditional probability PA in internal finitely additive probability space (X,ζ,P) is defined, and the conditional Loeb probability space (X,L(ζ,P) is derived by completion. Then the Loeb space (X,L(ζ,P),LP) is derived by completion of internal finitely additive probability space (X,ζ,P), and the conditional probability LP(A) in Loeb space (X,Lζ,P),LP) is defined. By dicussing the relationship of these two spaces, it is proved that L(ζ,PA)=L(ζ,p), and for ∀ B∊L(ζ,P),L(P) (B)=LP(A)(B). [ABSTRACT FROM AUTHOR]