We develop several applications to almost sure limit theorems for sums of independent vector valued random variables of an isoperimetric inequality due to Talagrand. A general treatment of the classical laws of large numbers of Kolmogorov and Prokorov and laws of the iterated logarithm of Kolmogorov and Hartman and Wintner is described. New results as well as simpler new proofs of known ones illustrate the usefulness of isoperimetric methods in this context. We show further how this approach can be used in the study of limit theorems for trimmed sums of independent and identically distributed random variables.