Chebyshev's theorem

Chebyshev's theorem is a name given to several theorems proven by Russian mathematician Pafnuty Chebyshev

• Bertrand's postulate
• Chebyshev's inequality
• Chebyshev's sum inequality
• The statement that if the function $\scriptstyle \pi (x)\ln x/x$ has a limit at infinity, then the limit is 1 (where π is the prime-counting function). This result has been superseded by the prime number theorem.

Unlike the Empricial Rule that can only be used with symmetric bell shaped distributions, Chebyshev's theorem can be used with any distribution.