Volume and multiplicities of real analytic sets

Guillaume Valette. "Volume and multiplicities of real analytic sets." Annales Polonici Mathematici 87.1 (2005): 265-276. <http://eudml.org/doc/280734>.

@article{GuillaumeValette2005,
abstract = {We give criteria of finite determinacy for the volume and multiplicities. Given an analytic set described by \{v = 0\}, we prove that the log-analytic expansion of the volume of the intersection of the set and a "little ball" is determined by that of the set defined by the Taylor expansion of v up to a certain order if the mapping v has an isolated singularity at the origin. We also compare the cardinalities of finite fibers of projections restricted to such a set.},
author = {Guillaume Valette},
journal = {Annales Polonici Mathematici},
keywords = {analytic sets; Hausdorff measure; stratification; sufficiency of jets},
language = {eng},
number = {1},
pages = {265-276},
title = {Volume and multiplicities of real analytic sets},
url = {http://eudml.org/doc/280734},
volume = {87},
year = {2005},
}

TY - JOUR
AU - Guillaume Valette
TI - Volume and multiplicities of real analytic sets
JO - Annales Polonici Mathematici
PY - 2005
VL - 87
IS - 1
SP - 265
EP - 276
AB - We give criteria of finite determinacy for the volume and multiplicities. Given an analytic set described by {v = 0}, we prove that the log-analytic expansion of the volume of the intersection of the set and a "little ball" is determined by that of the set defined by the Taylor expansion of v up to a certain order if the mapping v has an isolated singularity at the origin. We also compare the cardinalities of finite fibers of projections restricted to such a set.
LA - eng
KW - analytic sets; Hausdorff measure; stratification; sufficiency of jets
UR - http://eudml.org/doc/280734
ER -