Higher-order tangents and Fefferman’s paper on Whitney’s extension problem

Whitney [W2] proved that a function defined on a closed subset of R is the restriction of a C m function if the limiting values of all m th divided differences form a continuous function.We show that Fefferman's solution of Whitney's problem for R n [F, Th. 1] is equivalent to a variant of our conjecture in [BMP2] giving a criterion for C m extension in terms of iterated limits of finite differences.