During the late 50’s and early 60’s, the notion of Gauge integral was
presented by Kurzweil and Henstock, independently. The purpose of this paper
is to extend this concept to Summability theory. To accomplish this, we
introduce the notion of strongly summable to with
respect to Gauge by using measurable real valued function
defined on . \ We shall also prove inclusion
theorems to contrast it with other Summability integration techniques.