A simple proof of the discreteness of Dirichlet processes

That Dirichlet processes are discrete with probability 1 is demonstrated once more. And yes, these two pages spent fifty years in Norwegian.

💡 Research Summary

The note revisits a classic result in Bayesian non‑parametrics: a Dirichlet process DP(k · P₀) is almost surely discrete. After a brief historical survey that lists the many earlier proofs (Ferguson 1973‑74, Blackwell & MacQueen 1973, Sethuraman 1994, among others), the author presents a concise argument originally sketched in his 1976 Norwegian thesis.

The core tool is a lemma concerning the expectation of a measurable function f(P,X) when X is drawn from the random probability measure P. Formally,
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