Subadditive set function: Difference between revisions

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In mathematics, a '''subadditive set function''' is a [[set function]] whose value, informally, has the property that the value of function on the union of two sets is at most the sum of values of the function on each of the sets. This is thematically related to the [[subadditivity]] property of real-valued functions.

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== Definition ==

If <math>\Omega</math> is a [[set (mathematics)|set]], a subadditive function is a set function <math>f:2^{\Omega}\rightarrow \mathbb{R}</math>, where <math>2^\Omega</math> denotes the [[Power set#Representing subsets as functions|power set]] of <math>\Omega</math>, which satisfies the following inequality.<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 ==