# pr.probability – Example of a strictly proper scoring rule defined on the set of all probability measures on \$[0,1]\$

This question is closely related to another question I asked recently but is more to the point than that other question.

Let $$mathcal P$$ be the set of all probability measures on the Borel algebra of $$(0,1)$$. A measurable scoring rule $$S: mathcal P times (0,1) to (-infty, 0)$$ is called strictly proper if
$$int S(P,x)P(dx) > int S(Q, x)P(dx)$$
holds for all $$P neq Q$$ in $$mathcal P$$.

Can anyone provide a concrete example of a strictly proper scoring rule?