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{title2=$f(A)+f(B)\geq f(A\cup B)+f(A\cap B)$}
{wiki}

A <set function> is submodular if $f(A)+f(B)\geq f(A\cup B)+f(A\cap B)$ for every pair of subsets. <Entropy submodularity> is a fundamental example.

Submodular set function

Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 13 / 2 / i / Solution

Supermodular set function

Union-intersection compression

Submodular set function ( $f (A) + f (B) \geq f (A \cup B) + f (A \cap B)$ )

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Submodular set function (f(A)+f(B)≥f(A∪B)+f(A∩B))

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Submodular set function ( $f (A) + f (B) \geq f (A \cup B) + f (A \cap B)$ )

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