Measure Theoretic Zero Sets in Infinite Dimensional Spaces and Applications to Differentiability of Lip-Schitz Mappings
Measure-additive coverings and measurable selectors [Book]
Measure-determined enlargements of Boolean -algebras
Measures and Markov processes on function spaces
Measures of full dimension on self-affine sets
Measures of fuzziness and operations with fuzzy sets.
We discuss the effects that the usual set theoretic and arithmetic operations with fuzzy sets and fuzzy numbers have with respect to the energies and entropies of the fuzzy sets connected and of the resulting fuzzy sets, and we also compare the entropies and energies of the results of several of those operations.
Measures of maximal entropy for random -expansions
Let be a non-integer. We consider -expansions of the form , where the digits are generated by means of a Borel map defined on . We show that has a unique mixing measure of maximal entropy with marginal measure an infinite convolution of Bernoulli measures. Furthermore, under the measure the digits form a uniform Bernoulli process. In case 1 has a finite greedy expansion with positive coefficients, the measure of maximal entropy is Markov. We also discuss the uniqueness of -expansions....
Measures of sum-free intersecting families.
Measures on bundles and Trundles of measures
Measures on coallocation and normal lattices.
Measures on compact HS spaces
We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of . The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a . A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.
Measures on Corson compact spaces
We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.
Measures on groups with given projections
Measures on Product Spaces and the Existence of Strong Baire Liftings.
Measures on self-similar sets
Measures representable as -dimensional Hausdorff measures
Measures vectorielies, measures cylindriques et propriété de Radon-Nikodym
Measures which agree on balls.
Measures with finite semi-variation.
Measure-Theoretic Characterizations of Certain Topological Properties
It is shown that Čech completeness, ultracompleteness and local compactness can be defined by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.