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

On $\alpha$-covariance, long, short and negative memories for sequences of random variables with infinite variance