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The Gould integral in Banach lattices

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Abstract

In this paper, we study a Gould type integral in a new frame of Banach lattices. We consider the Gould integral of real functions relative to a non-additive set function taking values in a Banach lattice. Some continuity properties of this integral and relationships between integrability and total measurability are presented.

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Acknowledgments

The authors are very grateful to the unknown Referee for his valuable suggestions and for reporting Lemmas 2.4 and 2.5, Corollary 2.6 and a shorter proof of Theorem 3.2-VI.

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Authors and Affiliations

  1. Faculty of Mathematics, “Al. I. Cuza” University, Bd. Carol I, No. 11, Iaşi , 700506, Romania

    Alina Cristiana Gavriluţ & Anca Croitoru

  2. Department of Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploieşti, Bd. Bucureşti, No. 39, Ploiesti , 100680, Romania

    Alina Emilia Iosif

Authors
  1. Alina Cristiana Gavriluţ
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  2. Alina Emilia Iosif
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  3. Anca Croitoru
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Correspondence to Anca Croitoru.

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Gavriluţ, A.C., Iosif, A.E. & Croitoru, A. The Gould integral in Banach lattices. Positivity 19, 65–82 (2015). https://doi.org/10.1007/s11117-014-0283-7

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