# Subadditive function

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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 collection of subsets 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 $$f\left({ \cup_{i=1}^\infty A_i }\right) \le \sum_{i=1}^\infty f(A_i) \ .$$

How to Cite This Entry:
Subadditive function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subadditive_function&oldid=39139