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Singular Radon probabilities on $[0,1]^d$. Is conditioning on $x_i = \alpha$ well-defined?
$\newcommand{\B}{\mathcal B}$
First here, $[0,1]^d$ is a Polish space (i.e., a separable complete metric space). So, $[0,1]^d$ is a Radon space, and hence any (Borel) probability measure is Radon. So, …