4 Matching Results

Search Results

Results: 1 - 4
open access

Integrability, Measurability, and Summability of Certain Set Functions

Description: 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 Cha… more
Date: December 1977
Creator: Dawson, Dan Paul
Partner: UNT Libraries
open access

Valuations on Fields

Description: This thesis investigates some properties of valuations on fields. Basic definitions and theorems assumed are stated in Capter I. Chapter II introduces the concept of a valuation on a field. Real valuations and non-Archimedean valuations are presented. Chapter III generalizes non-Archimedean valuations. Examples are described in Chapters I and II. A result is the theorem stating that a real valuation of a field K is non-Archimedean if and only if $(a+b) < max4# (a), (b) for all a and b in K. Ch… more
Date: May 1977
Creator: Walker, Catherine A.
Partner: UNT Libraries
open access

Interpolation and Approximation

Description: In this paper, there are three chapters. The first chapter discusses interpolation. Here a theorem about the uniqueness of the solution to the general interpolation problem is proven. Then the problem of how to represent this unique solution is discussed. Finally, the error involved in the interpolation and the convergence of the interpolation process is developed. In the second chapter a theorem about the uniform approximation to continuous functions is proven. Then the best approximation and… more
Date: May 1977
Creator: Lal, Ram
Partner: UNT Libraries
open access

Complete Ordered Fields

Description: The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a … more
Date: August 1977
Creator: Arnold, Thompson Sharon
Partner: UNT Libraries
Back to Top of Screen