Document Zbl 1455.30042

Luna-Elizarrarás, M. E.; Pogorui, A.; Shapiro, M.; Kolomiiets, T.

On quaternionic measures. (English) Zbl 1455.30042

Adv. Appl. Clifford Algebr. 30, No. 4, Paper No. 63, 17 p. (2020).

The paper proposes a generalization of the notion of complex measure in the quaternionic setting. For such a generalization, the authors prove several founding results, such as:
– the finiteness of the modulus of variation (extending a Lemma originally stated by Rudin);
– a Lebesgue-type decomposition;
– a Radon-Nikodym type theorem;
– the fact that the set of quaternionic measures on a given domain is a Banch space.
These results are proven in many details and are treated very well.

Reviewer: Amedeo Altavilla (Ancona)

Cited in 1 Document

MSC:

30G35	Functions of hypercomplex variables and generalized variables
28A10	Real- or complex-valued set functions
28A33	Spaces of measures, convergence of measures

Keywords:

quaternions; measures; quaternionic measures

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References:

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