Kurzweil-Henstock Integral in Riesz spaces

Author(s): Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

DOI: 10.2174/978160805003110901010134

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(SL)-integral

Pp: 134-165 (32)

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Abstract

SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.

Abstract

In this chapter we deal with the strong Luzin ((SL)-) integral, related with the existence of primitives of functions in the weak sense. This integral is a variant of the Kurzweil-Henstock integral, which coincides with it in the real case, but is in general slightly different in the context of Riesz spaces, because some pathologies can occur. We also prove some versions of Hake and monotone convergence type theorems and of the Fundamental Theorem of Calculus, together with the basic properties.

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