Young-type integrals with respect to measurable processes

For positive real numbers p and q satisfying 1/p + 1/q > 1, it is known that if f (u) and g(u) have finite mean variations of orders p and q respectively, then an integral t s f (u)dg(u) exists in the Riemann sense.The present paper extends this Stieltjes integration theory, discussed by L. C. Young, to the case where f (u) and g(u) are measurable processes.Moreover, path-by-path piecewise-linear functions are constructed via Riemann-Stieltjes sums for measurable processes, and convergence theorems on such functions are derived.