M. Bricchi
abstract:
We shall consider the following problem: which
conditions should satisfy a function h : --> R in order to guarantee the
existence of a (regular) measure m in Rn
with compact subset G of Rn as support and
(*) c1h(r) <= m (B(g,
r)) <= c2 h(r),
for some positive constants c1, and c2 independent of
g in G and r, 0 < r < 1?
The theory of self-similar fractals provides outstanding examples of sets
fulfilling (*) with h(r) = rd, 0 <= d <= n, and a suitable measure
m. Analogously, we shall rely on some recent
techniques for the construction of pseudo self-similar fractals in order to deal
with our more general task.