A theorem of Hardy, Littlewood and Pólya and some related results for infinite vectors
Hazel Perfect · Mathematical Proceedings of the Cambridge Philosophical Society · 1967
We recall that a square matrix (finite or infinite) with non-negative elements and with each row-sum and column-sum equal to 1 is called doubly-stochastic (d.s.). If each row-sum and column-sum of a non-negative square matrix is less than or equal to 1, the matrix is called doubly-substochastic (d.s.s.).