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On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals

Antonio Boccuto, Beloslav Riečan (2004)

Czechoslovak Mathematical Journal

In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with...

On the modulus of measures with values in topological Riesz spaces.

Lech Drewnowski, Witold Wnuk (2002)

Revista Matemática Complutense

The paper is devoted to a study of some aspects of the theory of (topological) Riesz space valued measures. The main topics considered are the following. First, the problem of existence (and, particularly, the so-called proper existence) of the modulus of an order bounded measure, and its relation to a similar problem for the induced integral operator. Second, the question of how properties of such a measure like countable additivity, exhaustivity or so-called absolute exhaustivity, or the properties...

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