Gaussian Measure of Large Balls in $l_p$

Abstract

We study the behaviour of $\mu\{x \in E; \|x\| > t\}$ as $t \rightarrow \infty$ for a Gaussian measure $\mu$ in a Banach or quasi-Banach space in the following cases: 1. $E = l_p, 2 < p < \infty$, and $\mu$ of diagonal form but not necessarily symmetric; 2. $E =$ Hilbert space and $\mu$ arbitrary; 3. $E = l^n_p, 0 < p < 2$, and $\mu$ of diagonal form. While 2 solves a problem of Hweng (1980), 1 and 3 extend some results of Dobric, Marcus and Weber (1988).