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Ideal convergent subsequences and rearrangements for divergent sequences of functions

In: Mathematica Slovaca, vol. 67, no. 6
Marek Balcerzak - Michał Popławski - Artur Wachowicz
Detaily:
Rok, strany: 2017, 1461 - 1468
Kľúčové slová:
ideal convergence, Baire category, $\sigma$-finite measure, divergence almost everywhere, subsequences, rearrangement
O článku:
Let $\I$ be an ideal on $\N$ which is analytic or coanalytic. Assume that $(f_n)$ is a sequence of functions with the Baire property from a Polish space $X$ into a Polish space $Z$, which is divergent on a comeager set. We investigate the Baire category of $\I$-convergent subsequences and rearrangements of $(f_n)$. Our result generalizes a theorem of Kallman. A similar theorem for subsequences is obtained if $(X,\mu)$ is a $\sigma$-finite complete measure space and a sequence $(f_n)$ of measurable functions from $X$ to $Z$ is $\I$-divergent $\mu$-almost everywhere. Then the set of subsequences of $(f_n)$, $\I$-divergent $\mu$-almost everywhere, is of full product measure on $\{0,1}^\N$. Here we assume additionally that $\mathscr I$ has property (G).
Ako citovať:
ISO 690:
Balcerzak, M., Popławski, M., Wachowicz, A. 2017. Ideal convergent subsequences and rearrangements for divergent sequences of functions. In Mathematica Slovaca, vol. 67, no.6, pp. 1461-1468. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0062

APA:
Balcerzak, M., Popławski, M., Wachowicz, A. (2017). Ideal convergent subsequences and rearrangements for divergent sequences of functions. Mathematica Slovaca, 67(6), 1461-1468. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0062
O vydaní:
Publikované: 27. 11. 2017