10.4115/jla.v2i0.69

Abstract

Abstract:We introduce the notion of analytically and subanalytically tame measures. These are measures which behave well in the globally subanalytic context; they preserve tameness: integrals of globally subanalytic functions with parameters resp. analytic functions with parameters restricted to globally subanalytic compact sets are definable in an o-minimal structure. We consider the harmonic measure for a semianalytic bounded domain in the plane. We show that the harmonic measure for such a domain is analytically tame if the angles at singular boundary points are irrational multiples of π . If the domain is a polygon and the angles at singular boundary points are rational or Diophantine irrational multiples of π then the harmonic measure is subanalytically tame.2000 Mathematics Subject Classification 03C64, 30C85, 32B20 (primary)