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On additivity of mappings on measurable functions

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Abstract

We prove the additivity of regular l-additive mappings T: → [0,+∞] of a hereditary cone in the space of measurable functions on a measure space. Some examples are constructed of non-d-additive l-additive mappings T. The monotonicity of l-additive mappings T: → [0,+∞] is established. The examples are constructed of nonmonotone d-additive mappings T.

Let (S, +) be a commutative cancellation semigroup. Given a mapping T: → S, we prove the equivalence of additivity and l-additivity. It is shown that a strongly regular 2-homogeneous l-subadditive mapping T is subadditive. All results are new even in case = L +∞ .

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Authors and Affiliations

  1. Kazan Federal University, Kazan, Russia

    A. M. Bikchentaev

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  1. A. M. Bikchentaev
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Correspondence to A. M. Bikchentaev.

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Original Russian Text Copyright © 2014 Bikchentaev A.M.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 1, pp. 11–16, January–February, 2014.

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Bikchentaev, A.M. On additivity of mappings on measurable functions. Sib Math J 55, 7–11 (2014). https://doi.org/10.1134/S0037446614010029

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  • DOI: https://doi.org/10.1134/S0037446614010029

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