PomeDefinition 21.11.7.0ECB6CF7B06D Let $F_1,\ldots ,F_ m\in \mathrm{Conv}^{\mathrm{prop}}(N)$ ($m\in \mathbb {Z}_{>0}$). We define their infimal convolution $F_1 \square \cdots \square F_ m\in \mathrm{Conv}(N)$ as follows:
\[ F_1 \square \cdots \square F_ m(n)\coloneqq \inf \left\{ \sum _{i=1}^ m F_ i(n_ i):n_ i\in N, \sum _{i=1}^ m n_ i=n \right\} . \]
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