Rearrangement of series. The theorem of Levy-Steiniz. - José Bonet ...

Rearrangement of series
A rearrangement of the series � ak is the series � a π(k), where
is a bijection.
π : N → N
A series � ak is unconditionally convergent if the series � a π(k)
converges for each bijection π.
If the series � ak converges, the set of sums is
S( � ak) := {x ∈ R | x =
∞�
aπ(k) for some π}
k=1
It is the set of sums of all the rearrangements of the series.
José Bonet Rearrangement of series. The theorem of Levy-Steiniz.