Is marginal constraints equivalent to linear constraints?

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Edwinkumar
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If I have a set of Probability distributions on a product space with marginal constraints, is there any way to (how to) express the same as a linear family of PD's ( i.e. all [tex]P[/tex] s.t. [tex]E_P[ f_i] =a_i[/tex] for some [tex]f_i, a_i[/tex] )
 

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Could someone answer this?
 

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