 Define the class of polynomials π"n"(σ) to be those polynomials "p" of the "n"th degree for which

on some set of measure ≥ 2 contained in the closed interval [−1, 1+σ].Then the Remez inequality states that

where "T""n"("x") is the Chebyshev polynomial of degree "n", and the supremum norm is taken over the interval [−1, 1+σ].Observe that "T""n" is increasing on formula_3, hence 

The R.i., combined with an estimate on Chebyshev polynomials, implies the following
corollary