The absolute continuity of functions defined on the -ring generated by a ring
The atoms of a countable sum of set functions
The Hahn-Banach theorem implies the Banach-Tarski paradox
The Hausdorff a-Dimensional Measures of the Level Sets and the Graph of the TV-Parameter Wiener Process.
The Kantorovič-Rubinstein distance
The Kantorovič-Rubinstein distance
The Lebesgue integral a little over 100 years later.
The Necessity of Strongly Subadditive Capacities for Neyman-Pearson Minimax Tests.
The pathological infinity of measures
The Peano curves as limit of α-dense curves.
En este artículo presentamos una caracterización de las curvas de Peano como límite uniforme de sucesiones de curvas α-densas en el compacto que es llenado por la curva de Peano. Estas curvas α-densas deben tener densidades tendiendo a cero y sus funciones coordenadas deben de ser de variación tendiendo a infinito cuando α tiende a cero.
The quasi topology associated with a countably subadditive set function
This is a general study of an increasing, countably subadditive set function, called a capacity, and defined on the subsets of a topological space . The principal aim is the study of the “quasi-topological” properties of subsets of , or of numerical functions on , with respect to such a capacity . Analogues are obtained to various important properties of the fine topology in potential theory, notably the quasi Lindelöf principle (Doob), the existence of a fine support (Getoor), and the theorem...
The Sobolev capacity on metric spaces.
The (sub/super)additivity assertion of Choquet
The assertion in question comes from the short final section in Theory of capacities of Choquet (1953/54), in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this operation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and similarly for superadditivity. His treatment of this point was more like an outline, and his proof limited to a rather narrow special case. Thus the proper...
Thickness of a family of sets and uniform measures
Thin and fat sets for doubling measures in metric spaces
We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we give sufficient conditions for certain cut-out sets being thin or fat.
Topological properties of generalized Wallman spaces and lattice relations.
Two classes of measures
Two results for monocompact measures.
Two theorems on measurable sets and sets having the Baire property
Two-valued measure need not be purely -compact