Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures

V. I. Bogachev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 4, pp. 703-749

Résumé

This paper provides a survey of recent investigations connected with distributions of polynomials on multi- and infinite-dimensional spaces with measures. The most important results on estimates (independent of the number of variables) for distribution functions and integral norms and also on convergence of the distributions of polynomials in variation and in the Kantorovich metric are presented. Interesting open problems in this area at the junction of the theory of functions, probability theory, and measure theory are discussed. Bibliography: 131 titles.

Détail

Keywords: polynomials, distribution function, measurable polynomials, Gaussian measure, convex measure, logarithmically concave measure, Kantorovich metric.
Mots-clés : convergence in variation

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