for finite monotone sequences
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.
It is not important that and be non-negative. The proof consists of simply integrating the non-negative function over the square .
Chebyshev inequality. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_inequality&oldid=15534