... BOUNDS OF HAUSDORFF MEASURES OF TAME SETSTA LˆE LOI AND PHAN PHIENAbstract. In this paper we present some bounds of Hausdorff measures ofobjects definable in o-minimal structures: sets, fibers of ... subsets of Rmof degree ≤ d. Applying the BOUNDS OF HAUSDORFF MEASURES OF TAME SETS 45theorem, one gets the estimates from above, similar to Example 1, for thek-dimensional Hausdorff measures of algebraic ... followed by Proposition 1. BOUNDS OF HAUSDORFF MEASURES OF TAME SETS 43Corollary 1 (c.f. [Y-C] and [D-K]). Let A be a definable subset of Rmofdimension k. Then for any ball Bmrof radius r in Rm,Hk(A...