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Upper envelopes of inner premeasures

  • Heinz KönigEmail author
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Abstract

In the recent book [18] on measure and integration (cited as MI) and in subsequent papers [19] - [24] the present author attempted to restructure the domain of their basic extension and representation procedures, and to develop the implications on various issues in measure and integration and beyond. There were essential connections with the work [7] [8] of Gustave Choquet. Thus MI Section 10 obtained an extended version of his capacitability theorem. The representation theories in MI chapter V and [22] [24] were based on the Choquet integral introduced in [7] Section 48, in form of the so-called horizontal integral of MI Section 11, while [24] Section 1 obtained a comprehensive version of his fundamental theorem [7] 54.1. The present paper wants to resume another theme initiated in [7] Section 53.7, that is the representation of certain non-additive set functions and functionals as upper envelopes of appropriate measures.

Keywords

Submodular isotone set functions Inner premeasures Supportive properties 

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© Springer Basel 2012

Authors and Affiliations

  1. 1.MathematikUniversität des SaarlandesSaarbrücken (Allemagne)Germany

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