Source: Real Anal. Exchange
Volume 25, Number 2
This paper presents one of many interesting aspects of relatively convergent
series. Namely, given a sequence of elements of a Hilbert space we consider all
possible ways of placing plus or minus signs in front of these elements to
create an alternating sequence. In a convenient metric it makes sense to ask
what is the `size' of the set of those choices of $+$ or $-$ for which the
resulting series converges. The term `size' here refers to either Baire category
or Lebesgue measure of this set. It turns out that especially the question of
the Lebesgue measure of this set is quite intriguing and leads to interesting
results generalizing known results for real-valued sequence.
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