Chebyshev's inequality for Banach-space-valued random elements
Ling Zhou, Ze-Chun Hu

TL;DR
This paper extends Chebyshev's inequality to random elements in Banach spaces, providing a broader understanding of probabilistic bounds in infinite-dimensional spaces.
Contribution
It introduces a new generalization of Chebyshev's inequality specifically for Banach-space-valued random elements, expanding its applicability.
Findings
Derived a generalized Chebyshev's inequality for Banach spaces
Applicable to a wide class of Banach-space-valued random elements
Provides theoretical bounds for probabilistic analysis in Banach spaces
Abstract
In this paper, we obtain a new generalization of Chebyshev's inequality for random elements taking values in a separate Banach space.
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Taxonomy
TopicsProbabilistic and Robust Engineering Design · Optimal Experimental Design Methods · Statistical Distribution Estimation and Applications
