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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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Integrability of $\int \log(f(x)) f(x) dx$ for a probability density function $f$

I am looking for weak conditions when a probability density function $f$ on $\mathbb{R}^d$ has a finite integral $$ \int_{\mathbb{R}^d} \log(f(x)) f(x) dx. $$ Any references would be appreciated.