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Nonabsolutely convergent series

Dana Fraňková (1991)

Mathematica Bohemica

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 t [ 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.

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