In the study of sets of points certain sets are found to be negligible, especially when applied to the theory of functions. The purpose of this paper is to discuss three of these "negligible" types, namely, exhaustible sets, denumerable sets, and sets of Lebesgue measure zero. We will present a complete existential theory in q-space for the three set properties mentioned above, followed by a more restricted discussion in the linear continuum by use of interval properties.

The purpose of this paper is two-fold; we shall first establish a complete existential theory of functions of one real variable with respect to continuity, uniform continuity, absolute continuity, bounded variation, and Lipschitz condition, and second we shall study set-functions in a similar manner, except that the properties to be considered will be continuity, absolute continuity, bounded variation, and additivity.

It is our purpose here to investigate the method of solving equations for real roots by Newton's Method and to indicate a generalization arising from this method.

This thesis looks at power series, particularly in the areas of: radius of convergence, properties of functions represented by power series, algebra of power series, and Taylor's Theorem and continuation by means of power series.

The object of this paper is to consider necessary and sufficient conditions in order for certain important inequalities, which are frequently used in analysis, to reduce to equalities.