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→Examples of subadditive functions: Yes, they will end up being non-negative, but that's a consequence of the definition, not part of it. |
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== Definition ==
Let <math>\Omega</math> be a [[set (mathematics)|set]] and <math>f \colon 2^{\Omega} \rightarrow \mathbb{R}</math> be a [[set function]], where <math>2^\Omega</math> denotes the [[Power set#Representing subsets as functions|power set]] of <math>\Omega</math>. The function ''f'' is ''subadditive'' if for each subset <math>S</math> and <math>T</math> of <math>\Omega</math>, we have <math>f(S) + f(T) \geq f(S \cup T)</math>.<ref name="UF" /><ref name="DNS" />
== Examples of subadditive functions ==
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