Difference between revisions of "Subadditive function"
From Encyclopedia of Mathematics
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| − | A subadditive [[set function]] is a function $f$ on a | + | A subadditive [[set function]] is a function $f$ on a collection of subsets of a set $X$ with the property that |
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f(A \cup B) \le f(A) + f(B) \ . | f(A \cup B) \le f(A) + f(B) \ . | ||
Latest revision as of 06:33, 17 September 2016
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=39136
Subadditive function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subadditive_function&oldid=39136