Global ETD Search

1	Integrability, Measurability, and Summability of Certain Set Functions Dawson, Dan Paul 12 1900 (has links) The purpose of this paper is to investigate the integrability, measurability, and summability of certain set functions. The paper is divided into four chapters. The first chapter contains basic definitions and preliminary remarks about set functions and absolute continuity. In Chapter i, the integrability of bounded set functions is investigated. The chapter culminates with a theorem that characterizes the transmission of the integrability of a real function of n bounded set functions. In Chapter III, measurability is defined and a characterization of the transmission of measurability by a function of n variables is provided, In Chapter IV, summability is defined and the summability of set functions is investigated, Included is a characterization of the transmission of summability by a function of n variables. set functions absolute continuity in mathematics integrability of bounded set functions measurability of set functions Set functions.
2	Bounded sets in topological groups Chis, Cristina 09 February 2010 (has links) A boundedness structure (bornology) on a topological space is an ideal of subsets containing all singletons, that is, closed under taking subsets and unions of finitely many elements. In this paper we deal with the structure of the whole family of bounded subsets rather than the specific properties of them by means of certain functions that we define on a metrizable topological group. Our motivation is twofold: on the one hand, we obtain useful information about the structural features of certain remarkable classes of bounded systems, cofinality, local properties, etc. For example, we estimate the cofinality of these boundedness notions. In the second part of the paper, we apply duality methods in order to obtain estimations of the size of a local base for an important class of groups. This translation, which has been widely exhibited in the Pontryagin-van Kampen duality theory of locally compact abelian groups, is often very relevant and has been extended by many authors to more general classes of topological groups. In this work we follow basically the pattern and terminology given by Vilenkin in 1998. tightness Pontryagin-van Kampen duality theory duality theory invariant cardinals bornology boundedness bounded set general topology topological spaces harmonic analysis topological groups character weight cofinality local base 51 512 515.1 517

Search results

Integrability, Measurability, and Summability of Certain Set Functions

Bounded sets in topological groups