The set A is convex because the convex combination (t times one plus (1-t) times the other) of two coherent probability distributions remains a coherent probability distribution. This in turn is because the convex combination of two probability measures over a space of models (cf. definition 1) remains a probability distribution over the space of models.

I think, but am not sure, that your issue is looking at arbitrary points of [0,1]^{L'}, rather than the ones which correspond to probability measures.