On some analogs of Anderson’s inequality. (Russian) Zbl 0591.28010

Ilarionov, E. V.; Solntsev, S. A.

Teor. Veroyatn. Mat. Stat. 30, 56-59 (1984).

Let \(\mu\) be the Gauss centred measure on \(R^ n\), \(h\in R^ n\) and \(0\leq \alpha \leq \beta\). The authors prove that the inequality \(\mu (A+\alpha h)>\mu (A+\beta h)\) is satisfied for the set \(A=\cup^{n}_{k=1}(R^{k-1}\times [-\epsilon,\epsilon]\times R^{n- k})\) provided that \(\epsilon >0\) is sufficiently small. Similar inequality is obtained for \(R^{\infty}\). These results can be considered as analogs of Anderson’s inequality [T. W. Anderson, Proc. Am. Math. Soc. 6, 170-176 (1955; Zbl 0066.374)].

Reviewer: M.Navara

MSC:

28C20

Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)

Keywords:

Gauss centred measure; analogs of Anderson’s inequality

Citations:

Zbl 0066.374