Metric Entropy

AnalysisApproximationTheoryDynamicalSystemsFunctionalAnalysisGeometryProbabilityTheory Given a metric space and a subset , the metric or Kolmogorov-Sinai entropy of for fineness is where is the ε covering number of in . The metric entropy measures the degree of compactness of .

Dually, the entropy number of is the smallest needed to cover by epsilon balls: For a bounded linear operator between two Banach Spaces, the -entropy number of is the smallest such that the operator is compact for some set .