Expectation in metric spaces and characterizations of Banach spaces
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AbstractWe 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.
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2018 ◽
Vol 61
(1)
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pp. 33-47
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2016 ◽
Vol 68
(4)
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pp. 876-907
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2010 ◽
Vol 02
(04)
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pp. 581-597
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1979 ◽
Vol 2
(2)
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pp. 309-323
2021 ◽
Vol 151
(6)
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pp. 1683-1699
1997 ◽
Vol 20
(3)
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pp. 443-450
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