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Bounds of Hausdorff Measures of Tame Sets
Ta Le Loi, Phan Phien

 

Abstract

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, and so on. 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.