= Metric entropy
{title2=$H(\varepsilon,E)=\log N(\varepsilon,E)$}
= Kolmogorov entropy
{c}
{synonym}
For a subset $E$ of a <metric space>, its metric entropy at resolution $\varepsilon$ is the logarithm of the least number of radius-$\varepsilon$ balls covering $E$, with value infinity when no finite cover exists. It quantifies how many choices are needed to approximate an element at that resolution. If points are pairwise more than $2\varepsilon$ apart, each covering ball contains at most one, giving a lower bound by their logarithmic cardinality. The logarithm base changes only a constant factor. This approximation entropy differs from <Kolmogorov-Sinai entropy> of a dynamical system.
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