| Title:
|
Statistical convergence of infinite series (English) |
| Author:
|
Dindoš, M. |
| Author:
|
Šalát, T. |
| Author:
|
Toma, V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
989-1000 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we use the notion of statistical convergence of infinite series naturally introduced as the statistical convergence of the sequence of the partial sums of the series. We will discuss some questions related to the convergence of subseries of a given series. (English) |
| Keyword:
|
statistical convergence |
| Keyword:
|
set of the first category |
| Keyword:
|
Hausdorff dimension |
| Keyword:
|
homogeneous set |
| MSC:
|
40A05 |
| idZBL:
|
Zbl 1080.40500 |
| idMR:
|
MR2018844 |
| . |
| Date available:
|
2009-09-24T11:08:25Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127854 |
| . |
| Reference:
|
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| Reference:
|
[2] R. G. Cooke: Infinite Matrices and Sequence Spaces (Russian Edition).Moscow, 1960. MR 0126098 |
| Reference:
|
[3] M. Dindoš, I. Martišovitš and T. Šalát: Remarks on infinite series in linear normed spaces.Tatra Mt. Math. Publ. 19 (2000), 31–46. MR 1771020 |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
[9] T. Šalát: On Hausdorff measure of linear sets.Czechoslovak Math. J. 11 (86) (1980), 24–56. (Russian) MR 0153802 |
| Reference:
|
[10] T. Šalát: On subseries.Math. Zeit. 85 (1964), 209–225. MR 0179507, 10.1007/BF01112142 |
| Reference:
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| Reference:
|
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| Reference:
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[13] T. Šalát: On statistically convergent sequences of real numbers.Math. Slovaca 30 (1980), 139–150. MR 0587239 |
| Reference:
|
[14] I. J. Schoenberg: The integrability of certain functions and related summability methods.Amer. Math. Monthly 66 (1959), 361–375. Zbl 0089.04002, MR 0104946, 10.2307/2308747 |
| Reference:
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[15] C. Visser: The law of nought-or-one.Studia Math. 7 (1938), 143–159. Zbl 0019.22501, 10.4064/sm-7-1-143-149 |
| Reference:
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| Reference:
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| Reference:
|
[18] A. Zygmund: Trigonometric series I.MIR, Moscow, 1965. (Russian) MR 0178296 |
| . |
