# Article

 Title: Nonabsolutely convergent series (English) Author: Fraňková, Dana Language: English Journal: Mathematica Bohemica ISSN: 0862-7959 (print) ISSN: 2464-7136 (online) Volume: 116 Issue: 3 Year: 1991 Pages: 248-267 Summary lang: English . Category: math . Summary: Assume that for any $t$ from an interval $[a,b]$ a real number $u(t)$ is given. Summarizing all these numbers $u(t)$ is no problem in case of an absolutely convergent series $\sum_{t\in[a,b]}u(t)$. The paper gives a rule how to summarize a series of this type which is not absolutely convergent, using a theory of generalized Perron (or Kurzweil) integral. (English) Keyword: nonabsolutely convergent series Keyword: generalized Perron integral MSC: 26A39 MSC: 26A42 MSC: 40A05 idZBL: Zbl 0742.40002 idMR: MR1126447 DOI: 10.21136/MB.1991.126175 . Date available: 2009-09-24T20:45:33Z Last updated: 2020-07-29 Stable URL: http://hdl.handle.net/10338.dmlcz/126175 . Reference: [K] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a pararaeter.Czech. Math. Ј. 7 (82) (1957), 418-449. Reference: [S] Š. Schwabik: Generalized differential equations: Fundamental results.Rozpгavy ČSAV (95) (1985), No. 6. Zbl 0594.34002 .

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