The notion of the Kolmogorov-Sinaj entropy of a dynamical system
$(X, \Cal S, P, T)$ is based on measurable set partitions
$\Cal A=\{A_1, \dots, A_n\}$ and their entropy $H(\Cal
A)=-\Sigma P(A_i)\log P(A_i)$. The notion was extended by
many authors using partitions of unity, i.e., such
collections $(f_1,\dots, f_n)$ of non-negative measurable
functions that $\sum_{i=1}^n f_i=1_\Omega$. In this
contribution we extend this approach considering such
collections $(f_1,\dots, f_n)$ of non-negative measurable
functions that $\sum_{i=1}^n f_i^k=1_\Omega$.
