Integrals and derivatives of regularly varying functions in d and domains of attraction of stable distributions II.

A theorem on regularly varying functions in 2 is proved and applied to domains of attraction of stable laws with index 1 [less-than-or-equals, slant] [alpha] [less-than-or-equals, slant] 2. We also present a theory of [Pi]-variation in 2. Unlike the situation in 1 the latter is not connected with domain of attraction theory. The situation in d (d > 1) is more complicated but not essentially different; for simplicity we limit ourselves to 2. This article complements de Haan and Resnick (1979) where the situation for 0 < [alpha] < 1 was considered.