The Ultimate Chebyshev's sum inequality - American History Information Guide and Reference

Another article treats Chebyshev's inequality in probability theory.

In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if

$a_1 \geq a_2 \geq \cdots \geq a_n$

and

$b_1 \geq b_2 \geq \cdots \geq b_n,$

then

$n \sum_{k=1}^n a_kb_k \geq \left(\sum_{k=1}^n a_k\right)\left(\sum_{k=1}^n b_k\right).$

Chebyshev's sum inequality follows from the rearrangement inequality.

Last updated: 05-28-2005 22:49:15

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