On an inequality of A. Khintchine for zero-one matrices

Abstract

Let A be a matrix of m rows and n columns whose entries are either zero or one with row i of sum ri (i = 1, 2,…, m) and column j of sum sj (j = 1, 2,…, n). Then a result of Khintchine states that , where l = max(m, n) and σ is the total number of ones in A. In the present paper a new proof of Khintchine's inequality is presented and a number of extensions to bounded plane measurable sets are discussed.

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