  We discuss some formulae which express the Alexander polynomial (and thus the
zeta-function of the classical monodromy transformation) of a plane curve
singularity in terms of the ring of functions on the curve. One of them
describes the coefficients of the Alexander polynomial or of zeta-function of
the monodromy transformation as Euler characteristics of some explicitly
constructed spaces. For the Alexander polynomial these spaces are complements
to arrangements of projective hyperplanes in projective spaces. For the
zeta-function they are disjoint unions of such spaces. Under the influence of a
result by J.Denef and F.Loeser it was understood that this results are
connected with the notion of the motivic integration or rather with its version
(in some sense a dual one) where the space of arcs is substituted by the space
of functions. The aim of this paper is to discuss the notion of the integral
with respect to the Euler characteristics (or with respect to the generalized
Euler characteristic) over the space of functions (or over its
projectivization) and its connection with the formulae for the coefficients of
the Alexander polynomial and of the zeta-function of the monodromy
transformation as Euler characteristics of some spaces. The paper will be
published in Proceedings of the Steklov Mathematical Institute.
