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Chebyshev’s inequality for Banach-space-valued random elements. (English) Zbl 1245.60025

Summary: We obtain a new generalization of Chebyshev’s inequality for random elements taking values in a separable Banach space.

MSC:

60E15 Inequalities; stochastic orderings
60B11 Probability theory on linear topological spaces

References:

[1] Chen, X., 2007. A new generalization of Chebyshev inequality for random vectors. arXiv:0707.0805v1arXiv:0707.0805v2; Chen, X., 2007. A new generalization of Chebyshev inequality for random vectors. arXiv:0707.0805v1arXiv:0707.0805v2
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[7] Rao, B. L.S. P., Chebyshev’s inequality for Hilbert-space-valued random elements, Statistics & Probability Letters, 80, 1039-1042 (2010) · Zbl 1281.60008
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