Is marginal constraints equivalent to linear constraints? (1 Viewer)

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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] )
Could someone answer this?

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