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Extreme doubly stochastic measures with full support

Extreme doubly stochastic measures with full support

We give an elementary construction of doubly stochastic measures on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I times upper I"> <mml:semantics> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo>×<!-- × --></mml:mo> <mml:mi>I</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">I \times I</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with full support.