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Some Properties of a Lebesgue-Stieltjes Integral
It is the purpose of this paper to define a Lebesgue integral over a measurable set, the integration being performed with respect to a monotone non-decreasing function as in the Stieltjes integral, and to develop a few of the fundamental properties of such an integral.
Date:
1951
Creator:
Dean, Lura C.
System:
The UNT Digital Library
The Analytical Development of the Trigonometric Functions
This thesis is a study of the analytical development of the trigonometric functions.
Date:
1951
Creator:
Mackey, Pearl Cherrington
System:
The UNT Digital Library
Some Properties of Derivatives
This paper is concerned with certain properties of derivatives and some characterizations of linear point sets with derivatives. In 1946, Zygmunt Zahorski published a letter on this topic listing a number of theorems without proof, and no proof of these assertions has been published. Some of the theorems presented here are paraphrases of Zahorski's statements, developed in a slightly different order.
Date:
1951
Creator:
Dibben, Philip W.
System:
The UNT Digital Library
On Uniform Convergence
In this paper, we will be concerned primarily with series of functions and a particular type of convergence which will be described. The purpose of this paper is to familiarize the reader with the concept of uniform convergence. In the main it is a compilation of material found in various references and revised to conform to standard notation.
Date:
1951
Creator:
Drew, Dan Dale
System:
The UNT Digital Library
The Development of the Natural Numbers by Means of the Peano Postulates
This thesis covers the development of the natural numbers by means of the peano postulates.
Date:
1951
Creator:
Baugh, Orvil Lee
System:
The UNT Digital Library
Means and Mean Value Theorems
This study covers means, mean value theorems of the differential calculus, and mean value theorems of integral calculus.
Date:
1951
Creator:
Blummer, Raymond O.
System:
The UNT Digital Library
The Riemann Definite Integral of a Bounded Real Function
The object of this paper is to define, to establish necessary and sufficient conditions for the existence of, and to consider the elementary properties of the Riemann definite integral of a bounded function.
Date:
1950
Creator:
Hendrick, H. Wayne
System:
The UNT Digital Library
Semi-continuity and Related Properties
The elementary notion of a function originated in the work of mathematicians of the seventeenth century, and was somewhat closely connected with investigations in the field of algebra. This paper will be concerned with an investigation of a generalized type of continuity known as semi-continuity.
Date:
1950
Creator:
Huggins, Frank N.
System:
The UNT Digital Library
L'Hospital's Rule
The purpose of this paper is to present proofs for six cases of L'Hospital's Rule for the evaluation of indeterminate forms. It is also a purpose to reduce to one of these six cases some other indeterminate forms to which L'Hospital's Rule is applicable. In the course of presenting these proofs several theorems and definitions will be used without proof.
Date:
1950
Creator:
Spidell, William H.
System:
The UNT Digital Library
Planar Lebesgue Measure
This thesis attempts to prove the Lebesgue measure is a concrete realization of measure.
Date:
1950
Creator:
Martin, Nat G.
System:
The UNT Digital Library
Convergence Tests for Infinite Series
The field of infinite series is so large that any investigation into that field must necessarily be limited to a particular phase. An attempt has been made to develop a number of tests having a wide range of applications. Particular emphasis has been placed on tests for series of positive terms.
Date:
1950
Creator:
Latimer, Philip W.
System:
The UNT Digital Library
Some Properties of Dini Derivatives
The purpose of this paper is to derive certain of the fundamental properties of the Dini derivatives of an arbitrary real function. To this end it will be necessary to investigate the properties of the limits superior and inferior of real functions and to prove the Vitali Covering Theorem as well as a fundamental theorem on the metric density of arbitrary point sets.
Date:
August 1953
Creator:
Pinkerton, Jane W.
System:
The UNT Digital Library
Some Properties of the Perron Integral
The purpose of this thesis is to restate the definition of the integral as given by O. Perron, to establish some of the fundamental properties of the Perron integral, and to prove the equivalence between the Perron and Lebesgue integrals in the bounded case.
Date:
June 1955
Creator:
McWhorter, Bobby J.
System:
The UNT Digital Library
Some Results of Two Topological Spaces
This thesis explores some results of two topological spaces.
Date:
August 1955
Creator:
Boyd, James Robert
System:
The UNT Digital Library
Random Sampling
The purpose of this study is to show the use of random sampling in solving certain mathematical problems. The origin of random numbers to be used in sampling is discussed and methods of sampling from known distributions are then given together with an indication that the sampling procedures are unbiased.
Date:
January 1957
Creator:
Booker, Aaron Hicks
System:
The UNT Digital Library
Random Variables of One Dimension
This thesis examines random variables of one dimension.
Date:
August 1958
Creator:
Casler, Burtis Griffin
System:
The UNT Digital Library
A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions
The purpose of this paper is to define and develop a set of functions of an area in such a manner as to be analogous to the trigonometric and the hyperbolic functions.
Date:
August 1954
Creator:
Allen, Alfred I.
System:
The UNT Digital Library
Fundamental Properties of Fourier Series
This thesis is intended as an introduction to the study of one type of trigonometric series, the Fourier series.
Date:
August 1954
Creator:
Hubbard, Geogre U.
System:
The UNT Digital Library
The Lebesgue and Equivalent Integrals
The purpose of this thesis is to present a study of the Lebesgue definite integral, defined in four different ways.
Date:
August 1954
Creator:
Lewis, Leslie L.
System:
The UNT Digital Library
Exhaustibility and Related Set Properties
The purpose of this paper is to develop certain fundamental properties of exhaustible sets and their complements and to examine various set properties which are generalizations, with respect to exhaustible neglect, or well-known set properties.
Date:
1950
Creator:
Cargal, Buchanan
System:
The UNT Digital Library
Some Generalizations in the Theory of Summable Series
It will be our purpose to study a generalized definition of sum of a series and the restrictions which must be placed upon it in order that it shall satisfy the generally accepted requirements of any generalized definition of sum of a series. We shall then proceed to investigate the possibilities of further generalizing this process.
Date:
August 1950
Creator:
Penner, Jimmie G.
System:
The UNT Digital Library
Electronic Analog Computer Study of Effects of Motor Velocity and Driving Voltage Limits upon Servomechanism Performance
The object of this thesis is (1) to demonstrate the value of an electronic analog computer for the solution of non-linear ordinary differential equations particularly when a large family of solutions is required; and (2) to obtain as a by-product results of practical applicability to servomechanism selection and analysis.
Date:
1956
Creator:
Haynes, Joe Preston
System:
The UNT Digital Library
On Ordered Pairs of Cardinal Numbers
This thesis is on ordered pairs of cardinal numbers.
Date:
1957
Creator:
Dickinson, John Dean
System:
The UNT Digital Library
Some Fundamental Theorems on Infinite Products
Since infinite products are seldom encountered in elementary mathematics, it is the purpose of this paper to familiarize the reader with their concept and properties. In the main, it is the compilation of material found in various references and revised to conform to standard notation.
Date:
1957
Creator:
Gonzalez, Genaro B.
System:
The UNT Digital Library