GAUSSIAN RANDOM SETS IN BANACH SPACE
MADAN LAL PURI, Dan A. Ralescu, Stefan S. Ralescu · 2003
We define a Gaussian random set in a Banach space, and we prove the following characteriz ation theorem: Every Gaussian random •set can be represented as the sum of its expected value and a Gaussian mean zero random element.1. Introduction.The concept of random set (Robbins [16], [17]), Matheron [11]) has received considerable attention in recent years, partly motivated by geometric probability considerations and partly as an application of probability techniques in Banach space.The strong law of large numbers for random sets in R P was proved by Artstein and Vitale [1] and for random sets in Banach space by Puri and Ralescu [12], [13].The central limit theorem (CLT)