In the present paper, we are concerned with establishing precise connections between convergence in area, convergence in global or separate variations, and convergence in measure of the first partial derivatives of functions f(x, y) on a given rectangle R. Here f(x, u) denotes any summable function in R. The functions f(x, y) of bounded variation in the sense of Cesari, or BVC functions, are those defined geometrically by Cesari [ 1 l] in 1936, and variously designated as functions of generalized bounded variation in the sense of Tonelli, or gBVT. As proved by Krickeberg [ 171 in 1957, the BVC functions are those L-integrable functions f(x,~) whose first-order partial derivatives in the sense of distributions are measures. These BVC functions were used by Smoller and Conway [22] in 1966 to prove existence theorems for weak solutions of shock wave equations or conservative laws in several space variables. The same functions are the object of the theoretical study by Volpert [25 ] on spaces of such elements. The corresponding class of functions of generalized absolute continuity in the sense of Tone& or gACT, can also be defined geometrically. Alternatively, these functions are those L-integrable functions f(x, y) whose partial derivatives in the sense of distributions are L-integrable functions, and thus form the space H’,‘. For L-integrable functions f, or surfaces z =f(x,~), (x, y) E R, the area can be defined as an upper area, or generalized Lebesgue area, Lf, as in Cesari [ 111, where he proved that f has finite upper area Lf if and only iff is BVC. Alternatively, the area can be also delined as a lower area, as in [ 141, and as a Burkill-Cesari integral, af, as in [lo], where we proved that af is finite if and only iff again is BVC. Actually, Lf = af as we proved in [lo]. The present paper takes its motivation from previous work by many