Bounds of Hausdorff measures of tame sets
  In this paper we present some bounds of Hausdorff measures of objects definable in o-minimal structures: sets, fibers of maps, inverse images of curves of maps, etc. Moreover, we also give some explicit bounds for semi-algebraic or semi-Pfaffian cases, which depend only on the combinatoric data representing the objects involved. 
Ta Le Loi and Phan Phien
math.DG math.AG