This study of abstract measure covers classes of sets, measures and outer measures, extension of measures, and planer measure.

This thesis is a study of the analytical development of the trigonometric functions.

This thesis investigates atmospheric gusts and their effect on aircraft.

In this thesis, we shall attempt to present a study of certain properties of real functions related to the set property exhaustible.

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.

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.

This thesis discusses a development of the exponential and logarithmic functions.

This thesis covers the development of the natural numbers by means of the peano postulates.

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.

The primary purpose of this paper is to state a set of postulates for Boolean algebra and show the characteristic theorems derivable from them, and to unify in one paper the more important methods of representing Boolean algebra and show their equivalence.

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.

This thesis is intended as an introduction to the study of one type of trigonometric series, the Fourier series.

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.

In this paper a definitions shall be given for different types of improper integrals and several theorems concerning them shall be proved.

This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.

The purpose of this thesis is to provide a beginning graduate student in mathematics with the general theory underlying competition between rational, intelligent opponents. This competition can be described as a game of opposing strategies; hence, the name game theory.

This paper will be concerned with the convergence of complex power series.

The purpose of this thesis is to present a study of the Lebesgue definite integral, defined in four different ways.

This paper considers the concept of inner and outer content, which was introduced by Camille Jordan and Giuseppe Peano near the end of the nineteenth century.

This paper will be concerned with some fundamental properties of a line. In particular, fundamental ordering properties of a line segment are covered.

This study covers means, mean value theorems of the differential calculus, and mean value theorems of integral calculus.

The purpose of this paper is to describe the mechanization of the basic equations of motion for the performance and maneuver characteristics of an airplane with some simplifications which render solutions more practicable. The results of a study made to program these equations for calculation by the IBM MODEL 650 digital computer are presented as well as the steps to be taken in using this method of calculation.

This paper gives the derivation of a method for determining the forces to be applied to these points which will simulate the load distributed over all the airplane.

This thesis covers fundamental properties of metric spaces, as well as completeness, compactness, and separability of metric spaces.