As a beginner on $p$-adic analysis, I am trying to find (or construct) examples of $p$-adic distributions (and measures) and calculating some basic $p$-adic integrals. After a search, I found the following examples in the literature; Bernoulli measures by Mazur, Gamma measures by J. Diamond, and the measure defined as $(a+(p^N)) \mapsto z^a/(1-z^{p^N})$ by Koblitz. (I don't know if the final one has a special name).
I am also aware of Katz's Eisenstein measures, but it is an advanced example for now.
Are there any other well-known examples of $p$-adic distributions (and measures)?