X-Sets

Abstract

In this chapter, r always denotes a positive integer, and smoothness means C^{r smoothness. (However, the theorems II and II′ hold for r = ∞ and ω if we assume the property (II.1.8) for such r, which is clear by their proofs.) For its axiomatic treatment, the following definition of a subanalytic set, which is equivalent to the definition in §I.2, is adequate. The family of all subanalytic sets in Euclidean spaces is the smallest family & of subsets of Euclidean spaces which satisfies the following axioms}