Given a metric space , the metric entropy is where is the -covering number of ; see covering and packing.
Metric entropy is a measure of the complexity of the set . Typically diverges as , and we are interested in the rate at which it goes to zero.
Last modified Sep 02, 20241 min read
Given a metric space (X,ρ), the metric entropy is logN(δ;X,ρ) where N(δ;X,ρ) is the δ-covering number of (X,ρ); see covering and packing.
Metric entropy is a measure of the complexity of the set X. Typically N(δ) diverges as δ→0, and we are interested in the rate at which it goes to zero.