I have come across the following statement:
A notable feature of the Hierarchical Dirichlet Process is that all Dirichlet Processes' $G_j$ share the same set of atoms and only the atom weights differ. This is a result of the almost sure discreteness of the top-level DP.
What is meant by atom and atom weights? Googling gets to me Wiki articles about measure theory and I'm not able to understand them and also not sure if they are what I'm looking for.
Could anyone provide a simple explanation of their meaning?
