Subadditive function

Summary

A subadditive function is a function $f$ with $f(x + y) \le f(x) + f(y)$ for all $x, y$ in its domain. The triangle inequality says that every norm is subadditive, and every sublinear function is subadditive. For subadditive sequences, Fekete's lemma shows that $f(n)/n$ converges to its infimum, which may be $-\infty$. This makes subadditivity a basic tool for growth rates in analysis, combinatorics and ergodic theory.