Kurzweil and Henstock presented the notion of Gauge integral, independently. Using their definition Savas Patterson examined relationship between integral Summability theory. Because esoteric both theory, body literature is limited. As such only accessible to theories Pringsheim limits. The goal this paper present a natural multidimensional extension theory via methods. To accomplish we examine...

This paper considers ordered vector spaces with arbitrary closed cones and establishes a number of characterization results with applications to monotone comparative statics (Topkis (1978), Topkis (1998), Milgrom and Shannon (1994)). By appealing to the fundamental theorem of calculus for the Henstock-Kurzweil integral, we generalize existing results on increasing differences and supermodularit...

The dual space of the class of Henstock-Kurzweil integrable functions is well known in the one-dimensional case and corresponds to the space of multipliers which, in turn, coincides with the class of functions of bounded essential variation. Comparable results in higher dimensions have been elusive. For cases in which the partitions defining the Henstock-Kurzweil integrals are defined on n-cell...