The main results in this paper concern representing Lebesgue measure by nonstandard measures which avoid certain pathological sets. An (external) set $E$ is $S$-thin ...

Geometric measure theory provides a framework for analysing the interplay between geometric structures and measure, and is particularly adept at characterising the complexity of fractal sets through ...

This is a preview. Log in through your library . Abstract In the 1870s, Carl Neumann proposed the so-called method of the arithmetic mean for solving the Dirichlet problem on convex domains. Neumann's ...