Category measures on Baire spaces.
The purpose of this paper is to give a necessary and sufficient condition to define a category measure on a Baire topological space. In the last section we give some examples of spaces in these conditions.
Characterization of Baire-one functions between topological spaces
Characterizations of outer measures associated with lattice measures.
Christensen measurability of polynomial functions and convex functions of higher orders
Comparing measure theoretic entropy for -finite measures with topological entropy
Complete duals of C*(X).
Completion regularity and -additivity of measures on product spaces
Concerning a certain -algebra in compact Hausdorff spaces
Construction of non-subadditive measures and discretization of Borel measures
The main result of the paper provides a method for construction of regular non-subadditive measures in compact Hausdorff spaces. This result is followed by several examples. In the last section it is shown that “discretization” of ordinary measures is possible in the following sense. Given a positive regular Borel measure λ, one may construct a sequence of non-subadditive measures , each of which only takes a finite set of values, and such that converges to λ in the w*-topology.
Convex Corson compacta and Radon measures
Assuming the continuum hypothesis, we show that (i) there is a compact convex subset L of , and a probability Radon measure on L which has no separable support; (ii) there is a Corson compact space K, and a convex weak*-compact set M of Radon probability measures on K which has no -points.
Coverable Radon measures in topological spaces with covering properties
Coverable standard measures with the chain condition and the Lebesgue decomposition
Covering spaces and irreducible partitions
An irreducible partition of a space is a partition of that space into solid sets with a certain minimality property. Previously, these partitions were studied using the cup product in cohomology. This paper obtains similar results using the fundamental group instead. This allows the use of covering spaces to obtain information about irreducible partitions. This is then used to generalize Knudsen's construction of topological measures on the torus. We give examples of such measures that are invariant...
Criterios de convergencia de medidas de conjuntos Riemann integrables.
Décomposition des mesures selon la dimension
Density in the space of topological measures
Topological measures (formerly "quasi-measures") are set functions that generalize measures and correspond to certain non-linear functionals on the space of continuous functions. The goal of this paper is to consider relationships between various families of topological measures on a given space. In particular, we prove density theorems involving classes of simple, representable, extreme topological measures and measures, hence giving a way of approximating various topological measures by members...
Diferenciación de medidas vectoriales en semi-μ-espacios de Lusin.
Differentiation of implicit functions and Steinhaus' theorem in topological measure spaces
Duality of measure and category in infinite-dimensional separable Hilbert space .
Ein Beitrag zur Baire-Kategorie-Theorie.