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Moyennes des fonctions sous-analytiques, densité, cône tangent et tranches. (Means of sub-analytic functions, density, tangent cones and fibres). (French) Zbl 0694.32001
Real analytic and algebraic geometry, Proc. Conf., Trento/Italy 1988, Lect. Notes Math. 1420, 170-177 (1990).
[For the entire collection see Zbl 0686.00007.]
The paper deals with some metric properties of subanalytic sets, especially the density, defined as the limit of \(vol_ k(Y\cap B(y,r))/\sigma^ kr^ k\) as r tends to \(0^+\), where \(vol_ k\) is the Hausdorff measure, Y a subanalytic set of dimension k and \(\sigma^ kr^ k\) the volume of the transversal section of \(T(Y,r)=\{x\in {\mathbb{R}}^ n\); d(x,Y)\(\leq r\}.\)
It is shown that the density of a subanalytic set always exists and its properties are discussed.
Part 3 presents some applications to chains and currents, which are the field of the second and third author (cf. their Ph. D. thesis).
Reviewer: Z.Denkowska

32B20 Semi-analytic sets, subanalytic sets, and generalizations