I asked this at math.stackexchange.com, but got no answers. Let $ (X,B,\mu)$ be a probability space. Let $ T,S:X→X$ be two measurable measure preserving maps that commute (i.e $ TS=ST$ ). Let $ A$ be a (countable measurable) partition of $ X$ . Show that $ h(ST,A)≤h(S,A)+h(T,A)$ . If $ S=T$ , it’s rather easy.Read more