It is intuitive that our argument holds for all functions that fulfill the statistical relevancy condition, but intuition can be wrong. Let's move it to the discussion till further substantiated.
Furthermore, we assume that any measure shows gain if, and only if, evidence is observed assuming $P(E|H) > P(E|\neg{}H)$.
We refer to this assumption as "statistical relevance condition" [@wesleyc.salmonStatisticalExplanation1970; @fetzerStatisticalExplanations1974].
It is intuitive that our argument holds for all functions that fulfill the statistical relevancy condition, but intuition can be wrong. Let's move it to the discussion till further substantiated.