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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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Continuity of a minimizing measure w.r.t a parameter

Let $V_t(x)=x^2+t\phi(x)$ where $t>0$ and $\phi\in C^\infty_c(\mathbb{R})$. My question is what can be said about the continuity of the (unique) minimizer (among probability measures) of the following …
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