A categorical approach to integration.
A characterization of tribes with respect to the Łukasiewicz -norm
We give a complete characterization of tribes with respect to the Łukasiewicz -norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz -norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental -norms, e. g., for the product -norm.
A Decomposition Theorem for Additive Set-Functions, with Applications to Pettis Integrals and Ergodic Means.
A further investigation for Egoroff's theorem with respect to monotone set functions
In this paper, we investigate Egoroff’s theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff’s theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff’s theorem for non-additive measure is formulated in full generality.
A generalization of Steinhaus' theorem to coordinatewise measure preserving binary transformations
A generalization of Yano's extrapolation theorem
A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications
This paper presents a Komlós theorem that extends to the case of the set-valued Henstock-Kurzweil-Pettis integral a result obtained by Balder and Hess (in the integrably bounded case) and also a result of Hess and Ziat (in the Pettis integrability setting). As applications, a solution to a best approximation problem is given, weak compactness results are deduced and, finally, an existence theorem for an integral inclusion involving the Henstock-Kurzweil-Pettis set-valued integral is obtained.
A measurable selection theorem
A metric space associated with a probability space.
A Mixid Theory of Information - IV: Inset-Inaccuracy and Directed Divergence.
A necessary and sufficient condition for the representation of a function as a Hankel-Stieltjes transform
A note on almost sure convergence and convergence in measure
The present article studies the conditions under which the almost everywhere convergence and the convergence in measure coincide. An application in the statistical estimation theory is outlined as well.
A note on Carathéodory type function
A note on convergence of level sets.
A note on Lusin measurability in measure spaces
A note on Lusin's condition (N)
A note on measurable functions
A note on restricted measurability
A problem with almost everywhere equality
A topological space Y is said to have (AEEP) if the following condition is satisfied: Whenever (X,) is a measurable space and f,g: X → Y are two measurable functions, then the set Δ(f,g) = x ∈ X: f(x) = g(x) is a member of . It is shown that a metrizable space Y has (AEEP) iff the cardinality of Y is not greater than .
A -linear automorphism of the reals with non-measurable graph
This note contains a proof of the existence of a one-to-one function of onto itself with the following properties: is a rational-linear automorphism of , and the graph of is a non-measurable subset of the plane.