Abstract
Suppose that -∞ < a < b < ∞, a ≤u1n ≤ u2n ≤… ≤unn ≤ b, and a ≤ v1n ≤ v2n ≤ … ≤ vnn ≤ b for n ≥ 1.We simplify and strengthen Weyl's definition of equal distribution of by showing that the following statements are equivalent:(i) (ii) (iii) We relate this to Weyl's definition of uniform distribution and Szegö's distribution formula for the eigenvalues of a family of Toeplitz matrices and g is real-valued and continuous on [-π, π].
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