  Kwapien and Woyczynski asked in their monograph (1992) whether their notion
of superstrong domination is inherited when taking sums of independent
symmetric random vectors (one vector dominates another if, essentially, tail
probabilities of any norm of the two vectors compare up to some scaling
constants). We answer this question positively. As a by-product of our methods,
we establish that a certain notion of weak concentration is also preserved by
taking sums of independent symmetric random vectors.
