Concentration of measure
= Concentration of measure
For a <metric space> with a <probability measure> $\mu$, the concentration function is $\alpha(\varepsilon)=\sup_{\mu(A)\geq1/2}(1-\mu(A_\varepsilon))$, where $A_\varepsilon$ is the metric neighbourhood of radius $\varepsilon$. A sequence exhibits <concentration of measure> if these functions tend to zero for every fixed positive radius. The metric scale is part of this definition.