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 function $$S: \mathcal P \times [0,1] \to [-\infty, 0]$$ is called a strictly proper scoring rule 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?