Quasicontinuous Functions and Functions of Bounded Variation
Kay, Alvin J.
The purpose of this investigation is threefold. First, since quasicontinuous functions are a generalization of continuous functions, properties of quasicontinuous functions similar to the properties of continuous functions are stated and proved. Second, some of the properties of functions of bounded variation are stated and proved. Finally, the properties of quasicontinuous functions and functions of bounded variations are utilized in establishing the existence of the Cauchy Right, Cauchy Left, and the mean integral with respect to quasicontinuous functions and functions of bounded variation.
functions, bounded variation, integrals
Kay, A. J. (1965). Quasicontinuous functions and functions of bounded variation (Unpublished thesis). Southwest Texas State University, San Marcos, Texas.