# Clarifying the concept of a probability mass function

#### samr

##### New Member
I am trying to understand what is the relationship between the concept of a probability mass function, and that of a probability measure.

It seems to me that a probability mass function is simply a probability measure applied to a discrete random variable.

#### samr

##### New Member
If so, I have a follow up question : in the article on Random Variables and Probability Distributions in Britannica, it says

In the development of the probability function for a discrete random variable, two conditions must be satisfied: (1) f(x) must be nonnegative for each value of the random variable, and (2) the sum of the probabilities for each value of the random variable must equal one.
What about the 3d axiom of Kolmogorov?
If if A and B are mutually exclusive then :
P(A union B) = P(A) + P(B)

I have seen the same omission in a Coursera course I am taking.

(In this online resource however three properties are mentioned, and those three seem to correspond to Komogorov's 3 axioms )

#### schan

##### New Member
Yes, both PMF and Density Functions need to sum up to one for all values of R.V. X.

The set equation you have mentioned is also correct and non-conflicting from PMF/PDF definitions. What is your exact question here?

#### samr

##### New Member
Is the set equation required for PMF definition?