Probability Notation for p(x, theta|X) with Bayes theorem

Question

I'm trying to understand notation used to indicate probability densities, specifically using Bayes Theorem.

After a review of the continuous statement of the equation, the book I'm using shows how to relate the discrete to the continuous:

p(x |X ) = ∫p(x, θ |X )dθ

I understand that the first term is the stated using the words "The probability of the sample x given the population X", but I don't understand the multiple arguments in the next term. What is: p(x, θ|X)? I understand that θ represents the set of parameters defining the probability density, but the notation of p(a , b) is new to me - what is the logical meaning of this statement?

Thanks for the help!

Answer 1

After more online research, the answer to my question was basic and simple - the p(a, b) is the same as the probability of the union of a and b.