Entropy of a measurable decomposition
$\xi$ of a space with a normalized measure $(X,\mu)$
A concept defined as follows. If the elements of $\xi$ having measure zero form in total a set of positive measure, then the entropy of $\xi$ is $H(\xi)=\infty$; otherwise
where the sum is taken over all elements of $\xi$ of positive measure. The logarithm is usually to the base 2.
Instead of "measurable decomposition" the phrase "measurable partitionmeasurable partition" is often used, cf. [a1].
|[a1]||I.P. [I.P. Kornfel'd] Cornfel'd, S.V. Fomin, Ya.G. Sinai, "Ergodic theory" , Springer (1982) (Translated from Russian)|
Entropy of a measurable decomposition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Entropy_of_a_measurable_decomposition&oldid=33192