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Keywords:
Riesz spaces; capacities; integration; symmetric Choquet integral; monotone and dominated convergence theorems
Riesz spaces; capacities; integration; symmetric Choquet integral; monotone and dominated convergence theorems
Summary:
A definition of “Šipoš integral” is given, similarly to [3],[5],[10], for real-valued functions and with respect to Dedekind complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental properties and some convergence theorems for the Šipoš integral are proved.
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