Approximation of analytic sets by Nash tangents of higher order

The aim of this paper is to show that for every locally analytic subset X of C ^m and every there exist a neighborhood V of a in C ^m and a sequence of Nash subsets of V converging to such that X _ν and X satisfy a certain condition for tangency of order ν. Next it is shown that this condition implies that for sufficiently large ν the multiplicities of X _ν and X at a are equal.