Definition 3.107 . [02P1]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Definition 3.107.

Let $f_{1},\dots,f_{n}$ be concave functions on $N_{\mathbb{R}}$ . The mixed Monge-Ampère measure is defined by the formula

{\mathcal{M}}_{M}(f_{1},\dots,f_{n})=\frac{1}{n!}\sum_{j=1}^{n}(-1)^{n-j}\sum_{1\leq i_{1}<\cdots<i_{j}\leq n}{\mathcal{M}}_{M}(f_{i_{1}}+\dots+f_{i_{j}}).

It is a measure on $N_{\mathbb{R}}$ .