REMARKS ON THE PAPER \ON A PROBLEM OF A KHINCHIN-TYPE DECOMPOSITION THEOREM FOR EXTREME VALUES" BY E. PANCHEVA.

The paper contains an elegant approach for eliminating the problems caused by idempotents in the arithmetics of probability distribution functions over Rd where the operation is the coordinate wise maximum of the corresponding random vectors. This method is, in fact, an application of the general approach in Ruzsa and Szekely. In the article the notion of \hair"=\maximal idempotent divisor" H(s) for any element s in abstract semigroups S was introduced and a new semigroup H(s) S was considered to settle several problems much easier than directly in S, e.g., the characterization of the class max-I0.