**M. Bricchi**

##
Existence and Properties of h-Sets

**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 R^{n}
with compact subset G of R^{n} as support and

(*) c_{1}h(r) <= m (B(g,
r)) <= c_{2} h(r),

for some positive constants c_{1}, and c_{2} 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) = r^{d}, 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.