Chebyshev's theorem

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

• Bertrand's postulate, that for every n there is a prime between n and 2n.
• Chebyshev's inequality, on range of standard deviations around the mean, in statistics
• Chebyshev's sum inequality, about sums and products of decreasing sequences
• Chebyshev's equioscillation theorem, on the approximation of continuous functions with polynomials
• 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 This result has been superseded by the prime number theorem.