John: If you are doing it on purpose it doesn't "ruin" a thing, excuse me for not getting it. When searching for the formal concept analysis view of Galois Theory I stumbled, in the same conference [CLA11](http://cla2011.loria.fr/), with a talk of Dan Simovici defining partition entropy similarly as you say for his own purposes. But in PlanetMath [definition](http://planetmath.org/entropyofapartition) they do allow the measure \$$\mu\$$ to vary freely.