Given a purely atomic probability measure with support on n points, P, any mean-preserving contraction  of P, Q, with support on m > n points is a mixture of mean-preserving contractions of P, each with support on most n points. We illustrate an application of this result in economics.
Given a purely atomic probability measure with support on n points, P, any mean-preserving contraction (mpc) of P, Q, with support on m > n points is a mixture of mpcs of P, each with support on most n points. We illustrate an application of this result in economics.
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mean-preserving contractions
mpcs