On ideal equal convergence

Rafał Filipów; Marcin Staniszewski

Open Mathematics (2014)

  • Volume: 12, Issue: 6, page 896-910
  • ISSN: 2391-5455

Abstract

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We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]_and [Filipów R., Szuca P., Three kinds of convergence and the associated I-Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9]. We also solve a few problems posed in the paper by Das, Dutta and Pal.

How to cite

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Rafał Filipów, and Marcin Staniszewski. "On ideal equal convergence." Open Mathematics 12.6 (2014): 896-910. <http://eudml.org/doc/268976>.

@article{RafałFilipów2014,
abstract = {We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]\_and [Filipów R., Szuca P., Three kinds of convergence and the associated I-Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9]. We also solve a few problems posed in the paper by Das, Dutta and Pal.},
author = {Rafał Filipów, Marcin Staniszewski},
journal = {Open Mathematics},
keywords = {Ideal; P-ideal; Filter; Ideal convergence; Statistical convergence; Filter convergence; -convergence; Convergence of a sequence of functions; Equal convergence; Uniform convergence; Pointwise convergence; Sigma-uniform convergence; ideal; -ideal; filter; ideal convergence; statistical convergence; filter convergence; -convergence; convergence of a sequence of functions; equal convergence; uniform convergence; pointwise convergence; sigma-uniform convergence},
language = {eng},
number = {6},
pages = {896-910},
title = {On ideal equal convergence},
url = {http://eudml.org/doc/268976},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Rafał Filipów
AU - Marcin Staniszewski
TI - On ideal equal convergence
JO - Open Mathematics
PY - 2014
VL - 12
IS - 6
SP - 896
EP - 910
AB - We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]_and [Filipów R., Szuca P., Three kinds of convergence and the associated I-Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9]. We also solve a few problems posed in the paper by Das, Dutta and Pal.
LA - eng
KW - Ideal; P-ideal; Filter; Ideal convergence; Statistical convergence; Filter convergence; -convergence; Convergence of a sequence of functions; Equal convergence; Uniform convergence; Pointwise convergence; Sigma-uniform convergence; ideal; -ideal; filter; ideal convergence; statistical convergence; filter convergence; -convergence; convergence of a sequence of functions; equal convergence; uniform convergence; pointwise convergence; sigma-uniform convergence
UR - http://eudml.org/doc/268976
ER -

References

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  1. [1] Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472 Zbl0405.26006
  2. [2] Császár Á., Laczkovich M., Some remarks on discrete Baire classes, Acta Math. Acad. Sci. Hungar., 1979, 33(1–2), 51–70 http://dx.doi.org/10.1007/BF01903381 Zbl0401.54010
  3. [3] Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177 
  4. [4] Filipów R., Szuca P., Three kinds of convergence and the associated -Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9 http://dx.doi.org/10.1016/j.jmaa.2012.02.041 Zbl1247.26007
  5. [5] Hernández-Hernández F., Hrušák M., Cardinal invariants of analytic P-ideals, Canad. J. Math., 2007, 59(3), 575–595 http://dx.doi.org/10.4153/CJM-2007-024-8 Zbl1119.03046
  6. [6] Kostyrko P., Šalát T., Wilczyński W., -convergence, Real Anal. Exchange, 2000/01, 26(2), 669–685 
  7. [7] Mačaj M., Sleziak M., -convergence, Real Anal. Exchange, 2010/11, 36(1), 177–193 
  8. [8] Todorčevic S., Analytic gaps, Fund. Math., 1996, 150(1), 55–66 Zbl0851.04002

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