On approximation by polygons in the calculus of variations

We consider in this note questions of approximation having a bearing on variational problems, although the methods we use have no connection with those of the Calculus of Variations. The hypotheses we make are a good deal simpler than those generally made in variational problems. The results we obtain include as special cases certain parts of the theory of Weierstrass’s E-function, now called the theory of semi-continuity. But the information we obtain is much more precise.