# Chebyshev inequality

From Encyclopedia of Mathematics

*for finite monotone sequences*

The inequality

Chebyshev's inequality for monotone functions is the inequality

where and are either both increasing or both decreasing on .

The inequalities were established by P.L. Chebyshev in 1882.

#### Comments

It is not important that and be non-negative. The proof consists of simply integrating the non-negative function over the square .

**How to Cite This Entry:**

Chebyshev inequality.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_inequality&oldid=15534

This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article