Abstract: Let E be a Banach space with norm ---, and f: R2+ ?E a function with finite variation. Properties of the variation are studied, and an associated increasing real-valued function -f- is defined. Sufficient conditions are given for f to have properties analogous to those of functions of one variable. A correspondence f f between such functions and E-valued Borel measures on R2+ is established, and the equality - ?f -= ?-f- is...