Abstract

An integral for a scalar function with respect to a multimeasure N taking its values in a locally convex space is introduced. The definition is independent of the selections of N and is related to a functional version of the Bartle-Dunford-Schwartz integral with respect to a vector measure presented by Lewis. Its properties are studied together with its application to Radon-Nikodym theorems in order to represent as an integrable derivative the ratio of two general multimeasures or two dHd_H-multimeasures; equivalent conditions are provided in both cases.

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Keywords

  • Locally convex space
  • multifunction
  • Bartle-Dunford-Schwartz integral
  • support function
  • selection
  • Radon-Nikodym theorem

Mathematics Subject Classification

28B20; 26E25, 26A39, 28B05, 46G10, 54C60, 54C65

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Suggested citation

L. Di Piazza, K. Musiał, A. R. Sambucini. “Representations of Multimeasures via the Multivalued Bartle-Dunford-Schwartz Integral.” Journal of Convex Analysis 29 (2022), No. 4, 1119–1148. https://doi.org/10.68381/jca29062

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press LLC.