On the Lelong number of Whitney stratified sets
Polish Academy of Science
The Lelong number(or density) may be considered as a couterpart of the notion of multiplicity (used in complex algebraic geometry) for real analytic and algebraic sets. The Lelong number of a real analytic germ A (at 0) is defined as the limit (as r goes to zero) of the volume of A intersected with a ball of radius r (centered at 0) divided by the volume of this ball. I will explane that it varies continuously along the strata of a Whitney stratification.