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Given a family ${\mu }_{i\in I}$ on a Polish space (complete, separable metric space) $X$. When does there exist a measure $\lambda$ such that $$\mu_i=f_i \lambda$$ where the f_i are densities (Radon-Nikodym) of $mu_i$ wrt to $\lambda$. EDIT: What is a verifyable condition in the case I is uncountable. |
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Given a family ${\mu }_{i\in I}$ on a Polish space (complete, separable metric space) $X$. When does there exist a measure $\lambda$ such that $$\mu_i=f_i \lambda_i$$lambda$$ where the f_i are densities (Radon-Nikodym) of $mu_i$ wrt to $\lambda$. |
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common dominating measure for a family of measuresGiven a family ${\mu }_{i\in I}$ on a Polish space (complete, separable metric space) $X$. When does there exist a measure $\lambda$ such that $$\mu_i=f_i \lambda_i$$
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