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# For every <math>X\subseteq \Omega</math> and <math>x_1,x_2\in \Omega\backslash X</math> we have that <math>f(X\cup \{x_1\})+f(X\cup \{x_2\})\geq f(X\cup \{x_1,x_2\})+f(X)</math>.
A nonnegative submodular function is also a [[Subadditive set function|subadditive]] function, but a subadditive function need not be submodular.
== Types of submodular functions ==
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