Analytic Extensions of Differentiable Functions Defined in Closed Sets

A continuous extension the author has not seen in the literature may be given as follows; we assume for simplicity that A is bounded. Let h (r) (rO) be a continuous and monotone increasing function such that A (0) =0, and if x and y are any two points of A whose distance apart is rxv, then (x) -f (y) (rxv). For any points x of E and y of A, set B (x, y) =f (y) -h (rxi) ; then if x is in. 4, B (x, y) ᶠ (x). The continuous extension of f (x) is, F (x), which at each point x of equals the maximum of H (x, y) as y varies over A. 63