2
votes
1answer
417 views

Mandelbrot and “log-derivative”

I am reading Mandelbrot, and stubling upon his use of the limit ("almost a Hölder exponent") \lim_{\epsilon -> 0} log(f(x+\epsilon) - f(x))/log(\epsilon). To simplify, lets assume that f is ...
7
votes
2answers
498 views

local behavior of a finite Borel measure

Let $\mu$ be a finite Borel measure on $\mathbb{R}^n$. I am interested in how does $\mu(B(x,r))$ behave, where $B(x,r)$ is the open ball of radius $r$ centered at $x$. For instance, as far as I ...
5
votes
2answers
564 views

A calculus question related to quantization dimension

Going through some old papers, I came up with a simple-looking problem I thought about 5 years ago or so. MO wants motivation ... Associated to a probability measure on a metric space is something ...
3
votes
2answers
361 views

Systematization of deterministic and stochastic integrals

With this question I try to build up a systematization of different kinds of integrals. The following table differentiates between deterministic and stochastic integrals, the summation processes ...