On Approximation constants for Liouville numbers

We investigate some Diophantine approximation constants related to the simultaneous approximation of $(\zeta,\zeta^{2},\ldots,\zeta^{k})$ for Liouville numbers $\zeta$. For a certain class of Liouville numbers including the famous representative $\sum_{n\geq 1} 10^{-n!}$ and numbers in the Cantor set, we explicitly determine all approximation constants simultaneously for all $k\geq 1$.Comment: 12 page

Another Perron type integration in nn dimensions as an extension of integration of stepfunctions

summary:For a new Perron-type integral a concept of convergence is introduced such that the limit $f$ of a sequence of integrable functions $f_k$, $k \in \mathbb N$ is integrable and any integrable $f$ is the limit of a sequence of stepfunctions $g_k$, $k \in \mathbb N$