Difference between revisions of "Subadditive function"
From Encyclopedia of Mathematics
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f(x+y) \le f(x) + f(y) \ . | f(x+y) \le f(x) + f(y) \ . | ||
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| + | 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 | ||
| + | $$ | ||
| + | f\left({ \cup_{i=1}^\infty A_i }\right) \le \sum_{i=1}^\infty f(A_i) \ . | ||
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Latest revision as of 06:33, 17 September 2016
A real function $f$ with the property $$ 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=39134
Subadditive function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subadditive_function&oldid=39134