Expectaction in metric spaces and characterizations of Banach spaces

• Autorzy: Bator A. , Zięba W.
• Języki publikacji: EN

Abstrakty

EN

We consider different definitions of expectation of random elements taking values in metric spaces. All such definitions are valid also in Banach spaces and in this case the results coincide with the Bochner integral. There may exist an isometry between considered metric space and some Banach space and in this case one can use the Bochner integral instead of expectation in metric space. We give some conditions which ensure existence of such isometry, for two different definitions of expectation in metric space.

Słowa kluczowe

EN

Banach space; metric space; expectation

PL

przestrzeń Banacha; przestrzeń metryczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 4
• Strony: 901--908
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Bator A.

autor

Zięba W.

• Institute of Mathematics Marie Curie-Skłodowska University pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland,

Bibliografia

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• [5] K. T. Sturm, Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature, Ann. Probab. 30 (2002), 1195-1222.
• [6] P. Teran, I. Molchanov, The law of large numbers in a mertic space with a convex combination operation, J. Theoret. Probab. 19, 4 (2006), 875-897.