Measures and probabilities in ordered structures.

• Autores: Maria Assumpta Congost Iglesias
• Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 5, Nº. 1, 1981, págs. 45-68
• Idioma: español
• Títulos paralelos:
  • Medidas y probabilidades en estructuras ordenadas.
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• Resumen

  • This paper is concerned with lattice-group valued measures for which the sygma-additivity is defined by means of the order convergence properties. In the first section we treat the analogues for such order-measures with values in a Dedekind complete lattice-group of the Jordan, Lebesgue and Yosida-Hewitt descompositions. The second section deals with the construction of an integral for functions with respect to an order-measure, both taking their values in a Dedekind sygma-complete lattice-ring. Analogues of the monotone-convergence, dominated-convergence and Fatou theorems are obtained.