In this paper, iin Riesz spaces, firstly we show that the Riemann integral is equivalent to the Mengoli-Cauchy integral, and after we compare the monotone integral with other types of integrals. In particular, we introduce a Dunford-Schwartz-type integral and we prove that it coincides with the monotone integral, by virtue of the Vitali-type theorem for the (M)-integral.
Comparison between different types of abstract integral in Riesz spaces
BOCCUTO, Antonio;SAMBUCINI, Anna Rita
1997
Abstract
In this paper, iin Riesz spaces, firstly we show that the Riemann integral is equivalent to the Mengoli-Cauchy integral, and after we compare the monotone integral with other types of integrals. In particular, we introduce a Dunford-Schwartz-type integral and we prove that it coincides with the monotone integral, by virtue of the Vitali-type theorem for the (M)-integral.File in questo prodotto:
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