A Characterization of the Banach Spaces of Type p by Lévy Measures.
A characterization of the weak convergence of convolution powers
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 Characterization of Uniform Distribution
Is the Lebesgue measure on [0,1]² a unique product measure on [0,1]² which is transformed again into a product measure on [0,1]² by the mapping ψ(x,y) = (x,(x+y)mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y-I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous or discrete....
A Choquet Ordering and Unique Decompositions in Convex sets of Tight Measures
A class of Caratheodory outer measures in topological spaces
A class of continua that are not attractors of any IFS
This paper presents a sufficient condition for a continuum in ℝn to be embeddable in ℝn in such a way that its image is not an attractor of any iterated function system. An example of a continuum in ℝ2 that is not an attractor of any weak iterated function system is also given.
A class of convex non-coercive functionals and masonry-like materials
A class of generalized Ornstein transformations with the weak mixing property
A class of negatively fractal dimensional Gaussian random functions.
A class of sets whose distance set fills an interval
A classification of points on the Sierpinski gasket.
A combinatorial theorem on the existence of a separating element and its applications to sequences and -derivations of measures
A common generalization of Kelley's theorem (concerning measures on Boolean algebra) and on von Neumann's minimax theorem
A complete characterization of R-sets in the theory of differentiation of integrals
Let be the family of open rectangles in the plane ℝ² with a side of angle s to the x-axis. We say that a set S of directions is an R-set if there exists a function f ∈ L¹(ℝ²) such that the basis differentiates the integral of f if s ∉ S, and almost everywhere if s ∈ S. If the condition holds on a set of positive measure (instead of a.e.) we say that S is a WR-set. It is proved that S is an R-set (resp. a WR-set) if and only if it is a (resp. a ).
A complete metric on the space of integrable multifunctions
A concept of measurability for the Daniell integral
A conjecture of Ulam on the invariance of measures in Gilbert's cube
A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals
We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.
A continuity property of the dimension of the harmonic measure of Cantor sets under perturbations