On the basic representation theorem for convex domination of measures
Let \(P\) and \(Q\) be finite measures on \(\mathbb{R}^d\) with finite support. The main result uses a constructive proof to establish three statements, each of which is equivalent to the convex domination of \(Q\) by \(P\) (i.e., \(\int c dP\geq \int c dQ\) for every nonnegative convex function \(c\)). A second result shows how this result can be used to produce representation theorems for measures defined on infinite-dimensional spaces or which have infinite support. The latter result implies a number of well-known results, including a theorem of \textit{G. H. Hardy}, \textit{J. E. Littlewood} and \textit{G. Pólya} [Messenger Math. 58, 145-152 (1929; JFM 55.0740.04)].
scientific article; zbMATH DE number 1246329