McShane Integral of Functions With Values in a Ranked Countably Normed Space

Sergio  R. Canoy Jr.,

McShane Integral of Functions With Values in a Ranked Countably Normed Space

Abstract:

We shall define McShane integral of functions with values in a complete ranked countably normed space. We shall relate this definition to the definition given by Gordon for Banach-valued functions [2]. Further, we give some simple properlies of the integral and state its Cauchy criterion. As parlicular examples, we shall show that r-continuous functions and simple functions are McShane integrable.