Measurable uniform spaces
Measure and measurable functions of
Measure of noncompactness of subsets of Lebesgue spaces
Measure of nonhyperconvexity and fixed-point theorems.
Measure preserving analytic diffeomorphisms of countable dense sets in and
Measure Spaces Connected by Correspondences.
Measure theoretic behavior of closed sets
Measure theoretic zero sets in infinite dimensional spaces and differentiability of Lipschitz mappings
Measure-preserving maps
Measures of compactness in approach spaces
We investigate whether in the setting of approach spaces there exist measures of relative compactness, (relative) sequential compactness and (relative) countable compactness in the same vein as Kuratowski's measure of compactness. The answer is yes. Not only can we prove that such measures exist, but we can give usable formulas for them and we can prove that they behave nicely with respect to each other in the same way as the classical notions.
Measures of Lindelöf and separability in approach spaces.
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.
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.
Measure-theoretic characterizations of hereditarily-normal spaces.
Medias generalizadas y aplicaciones.
Meir-Keeler contractions of integral type are still Meir-Keeler contractions.
Menger curvature and Lipschitz parametrizations in metric spaces
We show that pointwise bounds on the Menger curvature imply Lipschitz parametrization for general compact metric spaces. We also give some estimates on the optimal Lipschitz constants of the parametrizing maps for the metric spaces in Ω(ε), the class of bounded metric spaces E such that the maximum angle for every triple in E is at least π/2 + arcsinε. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.
Menger curves in Peano continua
Menger's Theorem for topological spaces