Subadditive set function: Difference between revisions

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== Definition ==

IfLet <math>\Omega</math> isbe a [[set (mathematics)|set]], a subadditive function is a set functionand <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>, whichwe satisfieshave the<math>f(S) following+ inequalityf(T) \geq f(S \cup T)</math>.<ref name="UF" /><ref name="DNS" />

For every <math>S, T \subseteq \Omega</math> we have that <math>f(S)+f(T)\geq f(S\cup T)</math>.

== Examples of subadditive functions ==