Difference in Probability Measure vs. Probability Distribution I am trying to better understand the Difference in "Probability Measure" and "Probability Distribution"
I came across the following link : https://math.stackexchange.com/questions/1073744/distinguishing-probability-measure-function-and-distribution
" The difference between the terms "probability measure" and "probability distribution" is in some ways more of a difference in connotation of the terms rather than a difference between the things that the terms refer to. It's more about the way the terms are used. "
The answer over here suggests that these two concepts might be the same thing?
In this case - could we consider the "Normal Probability Distribution Function" as a "Probability Measure"?
Thanks!

A probability measure $P$ is a function which associates each event with its probability.
If the events are real Borel sets (nice sets of real numbers, such as intervals, finite sets etc) then in lieu of describing the probability measure (a task which is directly unwieldy) we can instead use a special kind of real valued function $F$ defined on the reals. This function is called as distribution function (or simply distribution) and it is defined so as to make $F(x)=P(-\infty,x]$. A mathematical theorem then guarantees the unique extension to the probabilities of other Borel sets.
From a probability theory perspective,  events are not Borel sets most of the time. However we may associate outcomes with real numbers (usually by some measurement) - this in turn induces an association of 'the practically useful events' to Borel sets; after which we proceed to use a distribution to describe the probabilities of these Borel sets.
