🚀 go-pugleaf

Here is a summary of the responses received.  Thanks to:
  bishop@math.sunysb.edu (Chris Bishop)
  stephen@mont.cs.missouri.edu (Stephen Montgomery-Smith)
  drobot@sjsumcs.sjsu.edu (Vladimir Drobot)

I asked:
>
>There is a theorem, probably due to Paul Levy, stated below.  Where can
>it be found in a modern textbook?
>
>If a series of independent (mean zero, say) random variables diverges a.s.,
>then applying a summation method won't help: it will still diverge a.s.

Two references were suggested.

(1) Theorem V.8.2 in Zygmund's _Trigonometric Series_ is the special case
   of the result for Rademacher series.

(2) Theorem 1 of Chapter II in J. P. Kahane, _Some random series of
   functions_ is a generalization to series with values in Banach space.
   Kahane does not give a reference for the theorem, but for the main lemma,
   he cites a paper of Levy.


-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)