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Let 2"eú)A(n) be a conditionally convergent series in a real Banach space B. Let S(h) denote the set of sums of the convergent rearrangements of this series. A well-known theorem of Riemann states that S (h) = B if B = R, the reals. A generalization of Riemann's Theorem, due independently to Levy [L] and Steinitz [S], states that if B is finite dimensional, then S(h) is a linear manifold in £ of dimension > 0. Another generalization of Riemann's Theorem [M] can be stated as an instance of thedoi:10.2307/1997989 fatcat:rvv7jltij5gbdhw5lt6flyn4fq