  We consider a measure of dependence for symmetric $\alpha$-stable random
vectors, which was introduced by the author in 1976. We demonstrate that this
measure of dependence can be extended for much more broad class of random
vectors (up to regularly varying vectors in separable Banach spaces). This
measure is applied for linear random processes and fields with heavy-tailed
innovations, for some stable processes, and these applications show that this
dependence measure, named as $\alpha$-covariance is a good substitute for the
usual covariance. Also we discuss a problem of defining long, short, and
negative memories for stationary processes and fields with infinite variances.
