Alternative definitions of -density topology
Amoeba relation and Galois-Tukey connections
An abstract and generalized approach to the Vitali theorem on nonmeasurable sets
Here we present abstract formulations of two theorems of Solecki which deal with some generalizations of the classical Vitali theorem on nonmeasurable sets in spaces with transformation groups.
An Abstract Approach to Weak Topologies in Spaces of Measures
An addendum to a remark on Slutsky's theorem
An algebraic and logical approach to continuous images
An alternative concept of the n-dimensional measure
An analog of Sard's theorem for -smooth functions of two variables.
An analogue of a result of Carathéodory
An analytic study on the self-similar fractals: Differentiation of integrals.
An Application of Shoenfield's Absoluteness Theorem to the Theory of Uniform Distribution.
An approximate analog of a theorem of Khintchine
An area formula in metric spaces
We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure-theoretic notion of Jacobian, defined as the density of a suitable "pull-back measure". Finally, we give some applications and examples.
An elementary proof of Hawkes's conjecture on Galton-Watson trees.
An elementary proof of Komlós-Révész theorem in Hilbert spaces.
An elementary proof of the Fubini-Stone theorem
An Equipartition of Planar Sets.
An exact functional Radon-Nikodym theorem for Daniell integrals
Given two positive Daniell integrals I and J, with J absolutely continuous with respect to I, we find sufficient conditions in order to obtain an exact Radon-Nikodym derivative f of J with respect to I. The procedure of obtaining f is constructive.
An example concerning automorphisms of generalized cubes
An existence result on partitioning of a measurable space: Pareto optimality and core
This paper investigates the problem of optimal partitioning of a measurable space among a finite number of individuals. We demonstrate the sufficient conditions for the existence of weakly Pareto optimal partitions and for the equivalence between weak Pareto optimality and Pareto optimality. We demonstrate that every weakly Pareto optimal partition is a solution to the problem of maximizing a weighted sum of individual utilities. We also provide sufficient conditions for the existence of core partitions...