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# Proof: The proof is identical to the finite case of Theorem 1.22.

DOI link for Proof: The proof is identical to the finite case of Theorem 1.22.

Proof: The proof is identical to the finite case of Theorem 1.22. book

# Proof: The proof is identical to the finite case of Theorem 1.22.

DOI link for Proof: The proof is identical to the finite case of Theorem 1.22.

Proof: The proof is identical to the finite case of Theorem 1.22. book

## ABSTRACT

If we wish to constructively prove that the extreme points of D are exactly the permutation operators, we must begin with a doubly stochastic matrix P with an entry pmn (0, ], From this we need to construct doubly stochas tic matrices A = (aij) and B = (bij) such that 1/2 (aij + bij) = pij Ai, j . The following proof of the following Lemma was suggested by a technique used by Mauldon and it is essential in this construction.