New Versions of Some Classical Stochastic Inequalities.

Motivated by an investigation of finding necessary and sufficient conditions for the Kolmogorov strong law of large numbers for the general Gini's mean difference, new versions of the classical Lévy, Ottaviani, and Hoffmann-J\ooTrgensen inequalities are obtained for a sequence of Banach space valued random variables. No geometric conditions are imposed on the Banach space. An application to the general Gini's mean difference in a Banach space setting is presented. [ABSTRACT FROM PUBLISHER]