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nonabsolutely convergent series; generalized Perron 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.
[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 0594.34002
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