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The function $P$ that takes an event $A$ as input and returns the probability $P(A)$ as output is called a "probability measure" when we are developing probability using measure theory.

I have also seen some authors use the term "probability law". (I think Bertsekas uses this term.)

I think it is fairly common to refer to $P$ as a "probability distribution", but there is an issue here that I want to be careful about: I have seen that some authors use the term "distribution" only when referring to the distribution of a random variable $X$. For example, I believe that Folland makes this distinction. Should I make this distinction also in an undergraduate probability course (that does not use measure theory)?

What is the best or most standard term to use instead of "probability measure" in an introduction to probability course?

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  • $\begingroup$ A good piece of advice is to follow the terminology of the textbook we are using, but I'm also interested in understanding if my textbook is using the best terminology. $\endgroup$
    – eternalGoldenBraid
    Jul 19, 2018 at 16:01
  • $\begingroup$ Are you asking about a priori or a posteriori probabilities? $\endgroup$
    – Jasper
    Jul 20, 2018 at 2:35
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    $\begingroup$ I hope whoever answer this gives it 110%. $\endgroup$
    – James S. Cook
    Jul 21, 2018 at 23:37
  • $\begingroup$ @Jasper I'd like to know the best synonym for "probability measure" to use in an undergraduate introduction to probability course. It seems like a good idea to avoid using the word "measure" in a class that does not use measure theory. Perhaps "probability distribution" is the simple answer, but the terminology does not seem to be quite standard, as can be seen on this Wikipedia page. The textbook I'm using uses the term "probability set function", which I don't think is a very standard term. $\endgroup$
    – eternalGoldenBraid
    Jul 22, 2018 at 1:42
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    $\begingroup$ If you want to avoid saying "measure", speak of the "probability function" or simply the "probability". Another way to deal with this issue is to avoid speaking of $P$ in the abstract, always referring to $P(A)$ or $P(A|B)$, the probability of the event $A$ or the conditional probability of $A$ given $B$. $\endgroup$
    – Dan Fox
    Jul 24, 2018 at 9:52

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