Geodesic
Nonabsolutely convergent series
Mathematica Bohemica, Tome 116 (1991) no. 3, pp. 248-267

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MR Zbl
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.
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.
DOI : 10.21136/MB.1991.126175
Classification : 26A39, 26A42, 40A05
Keywords: nonabsolutely convergent series; generalized Perron integral 
Fraňková, Dana. Nonabsolutely convergent series. Mathematica Bohemica, Tome 116 (1991) no. 3, pp. 248-267. doi: 10.21136/MB.1991.126175
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[K] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a pararaeter. Czech. Math. Ј. 7 (82) (1957), 418-449.

[S] Š. Schwabik: Generalized differential equations: Fundamental results. Rozpгavy ČSAV (95) (1985), No. 6. | Zbl

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