View source for Subadditive function

A real function $f$ with the property
$$
f(x+y) \le f(x) + f(y) \ .
$$

A subadditive [[set function]] is a function $f$ on a collections of subset of a set $X$ with the property that
$$
f(A \cup B) \le f(A) + f(B) \ .
$$
A set function is $\sigma$-''subadditive'' or ''countably subadditive'' if 
$$
f\left({ \cup_{i=1}^\infty A_i }\right) \le \sum_{i=1}^\infty f(A_i) \ .
$$