Rearranging series of vectors on a small set
نویسندگان
چکیده
منابع مشابه
Rearranging Series Constructively
Riemann’s theorems on the rearrangement of absolutely convergent and conditionally convergent series of real numbers are analysed within Bishop-style constructive mathematics. The constructive proof that every rearrangement of an absolutely convergent series has the same sum is relatively straightforward; but the proof that a conditionally convergent series can be rearranged to converge to what...
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We consider ideals I of subsets of the set of natural numbers N such that for every conditionally convergent series of real numbers ∑ n∈N an and s ∈ R, then there is a sequence of signs δ = (δn)n∈N such that ∑ n∈N δnan = s and N(δ) := {n ∈ N : δn = −1} ∈ I. We give some properties of such ideals and characterize them in terms of extendability to a summable ideal.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2014.11.059