Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces
The convergence in mean of a weighted sum ∑kank(Xk−EXk) of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the {ank}-compactly uniform integrability of {Xn}. This condition, which is implied by...
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000604 |
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| _version_ | 1849305415516422144 |
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| author | M. Ordóñez Cabrera |
| author_facet | M. Ordóñez Cabrera |
| author_sort | M. Ordóñez Cabrera |
| collection | DOAJ |
| description | The convergence in mean of a weighted sum ∑kank(Xk−EXk) of random
elements in a separable Banach space is studied under a new hypothesis which relates the random
elements with their respective weights in the sum: the {ank}-compactly uniform integrability
of {Xn}. This condition, which is implied by the tightness of {Xn} and the {ank}-uniform
integrability of {‖Xn‖}, is weaker than the compactly miform integrability of {Xn} and leads
to a result of convergence in mean which is strictly stronger than a recent result of Wang, Rao
and Deli. |
| format | Article |
| id | doaj-art-07afd88ca842469ba722893cd257bb9a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-07afd88ca842469ba722893cd257bb9a2025-08-20T03:55:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120344345010.1155/S0161171297000604Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spacesM. Ordóñez Cabrera0Department of Mathematical Analysis, University of Sevilla, Sevilla, SpainThe convergence in mean of a weighted sum ∑kank(Xk−EXk) of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the {ank}-compactly uniform integrability of {Xn}. This condition, which is implied by the tightness of {Xn} and the {ank}-uniform integrability of {‖Xn‖}, is weaker than the compactly miform integrability of {Xn} and leads to a result of convergence in mean which is strictly stronger than a recent result of Wang, Rao and Deli.http://dx.doi.org/10.1155/S0161171297000604weighted sumsrandom elements in separable Banach spacescompactly uniform integrability{ank}-compactly uniform integrabilitytightness{ank}- uniform integrabilityconvergence in mean. |
| spellingShingle | M. Ordóñez Cabrera Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces International Journal of Mathematics and Mathematical Sciences weighted sums random elements in separable Banach spaces compactly uniform integrability {ank}-compactly uniform integrability tightness {ank}- uniform integrability convergence in mean. |
| title | Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces |
| title_full | Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces |
| title_fullStr | Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces |
| title_full_unstemmed | Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces |
| title_short | Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces |
| title_sort | convergence in mean of weighted sums of an k compactly uniformly integrable random elements in banach spaces |
| topic | weighted sums random elements in separable Banach spaces compactly uniform integrability {ank}-compactly uniform integrability tightness {ank}- uniform integrability convergence in mean. |
| url | http://dx.doi.org/10.1155/S0161171297000604 |
| work_keys_str_mv | AT mordonezcabrera convergenceinmeanofweightedsumsofankcompactlyuniformlyintegrablerandomelementsinbanachspaces |