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of the surface z=f(x, y), where (1.2) f(x, y) is everywhere a continuous and one-valued function of (x, y). Now let {S(fn, P)} be a sequence of polyhedra inscribed to S(f, P) such that (1.3) fn(x, y) is a linear function of x and y on every triangle in some triangulation(l) T3n(P) of P, and fn(x, y) —f(x, y) at every vertex of cBn(P) ; (1.4) the greatest diameter of any triangle of 15n(P) tends to 0 as n—><x>. Denoting by E(fn, P) the area of S(fn, P) (in the elementary sense), we define

On Geöcze’s problem for non-parametric surfaces