For the extended mean Stieltjes
integral R. A. Stokes has shown that joint discontinuities of the functions involved
can be ignored just as in the ordinary mean Stieltjes integral as considered by
Porcelli and others. A Stieltjes type integral of a function with respect to a function
pair has been defind by E. D. Roach, but existence of the integral depends upon the
simultaneous continuity of two or more of the functions involved. In this paper a
mean Stieltjes type integral of a function with respect to a function pair is defined
which overcomes these limitations. Representation theorems for the integral are also
given.
