Kolmogorov epsilon-entropy

Summary

Let $K$ be a totally bounded set in a metric space. Its Kolmogorov $\varepsilon$-entropy is the binary logarithm of the least number of pieces of diameter at most $2\varepsilon$ needed to cover $K$. It measures how many bits are needed to describe an element of $K$ to accuracy $\varepsilon$. Kolmogorov and Tikhomirov studied its growth as $\varepsilon \to 0$ for classes of smooth and analytic functions. It gives lower bounds for every method of approximation or coding of the class, linear or not.