Existence of probability measures with given marginals. (English) Zbl 0739.60001

The authors discuss the following problem: Let \(\lambda\) be a finite measure, let \(0\leq f\leq 1\) be a measurable real function and let \(\pi_ j\), \(1\leq j\leq N\), be \(N\) measurable functions. Under which conditions on \(\lambda\) can one find a measurable function \(g\) with values only 0 and 1 such that the distributions of \(\pi_ j\), \(1\leq j\leq N\), are the same for the measures with density \(f\) and with density \(g\)? The case of linear projections on \(\mathbb{R}^ p\) has a relation to a problem in tomography.


60A10 Probabilistic measure theory
52A40 Inequalities and extremum problems involving convexity in convex geometry
28A35 Measures and integrals in product spaces
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