Boolean algebras and uniform convergence of series

Several classical results on uniform convergence of unconditionally Cauchy series are generalized to weakly unconditionally Cauchy series. This uniform convergence is characterized through subalgebras and subfamilies of P(N). A generalization of the Orlicz–Pettis theorem is also proved by mean of su...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2003-08, Vol.284 (1), p.89-96
Main Authors: Aizpuru, A., Gutiérrez-Dávila, A., Pérez-Fernández, F.J.
Format: Article
Language:English
Subjects:
Algebraic logic
Boolean algebras
Combinatorics. Ordered structures
Exact sciences and technology
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
Order, lattices, ordered algebraic structures
Sciences and techniques of general use
Unconditionally Cauchy series
Uniform convergence
Weakly unconditionally Cauchy series
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Summary:Several classical results on uniform convergence of unconditionally Cauchy series are generalized to weakly unconditionally Cauchy series. This uniform convergence is characterized through subalgebras and subfamilies of P(N). A generalization of the Orlicz–Pettis theorem is also proved by mean of subalgebras of P(N).
ISSN:0022-247X
1096-0813
DOI:10.1016/S0022-247X(03)00241-5