Abstract
For an arbitrary sequence of events and an integer
we study the problem whether
implies either
or
It is partially solved using both probabilistic and nonprobabilistic arguments. The First and Second Borel-Cantelli Lemmas are both used to show that the implication holds if m = 1 and an equivalent formulation concerning a real series problem is presented. That the implication does not hold if m = 2 is shown using a real series and it is an open problem for
Some other open problems are also presented and discussed.