Abstract
Some subsequence {f nk }k∈N converges uniformly on compact subsets of Ω. Thus each of the sequences \(S_p \mathop = \limits^{{\text{def}}} \left\{ {f_{n_k }^{2^p } } \right\}_{k \in {\text{N}}} {\text{,}}\,p \in \mathbb{Z}^ + \) converges on compact subsets of Ω. Furthermore, S p+1 ⊂ S p . The diagonal sequence \(S\mathop = \limits^{{\text{def}}} \left\{ {f_{n_p }^{2^p } } \right\}p \in {\text{N}}\) is a subset of S 0.
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© 1992 Springer Science+Business Media New York
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Gelbaum, B.R. (1992). Families of Functions. In: Problems in Real and Complex Analysis. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0925-6_29
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DOI: https://doi.org/10.1007/978-1-4612-0925-6_29
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6949-6
Online ISBN: 978-1-4612-0925-6
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