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Is the probability density function (pdf) unique?

For example, I've seen the pdf of the uniform distribution written in two different versions, one with strict inequality and the other is not strict. From the definition, pdf is a function $f$ such that $P(X\in B)=\int_B f$. So it seems that the value of $x$ at one particular point doesn't really matter. Am I correct?

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    Depends. If your pdf has a point mass somewhere, it would matter. For example, a mixture of half a uniform distribution, and a $0.5$ point mass at $x$, then the CDF would have a "jump" at $x$.2012-03-18

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