Geodesic
On the existence of probability distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 620-627

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Let $X=\{0,\ldots, n-1\}$ and $\Gamma=\{(x_1,\ldots, x_s)\}\in X^s\colon\,\sum_{\sigma=1}^s x_\sigma=n-1$. For the marginals of probability distributions on $\Gamma$ with the additional property of forming an $s$-tuple of decreasing probabilities on $X$ a simple characterization is given. This has an interesting application to asymptotic spectra in the sense of Strassen [J. Reine Angew. Math., 384 (1988), pp. 102–152; 413 (1991), pp. 127–180]. Some correlated questions are discussed in an appendix.
Keywords: probability law, marginal distribution, asymptotic spectra in the sense of Strassen. 
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     title = {On the existence of probability distributions},
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F. Mauch. On the existence of probability distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 620-627. http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a13/