Chebyshev's inequality for Banach-space-valued random elements

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.