  In this note, based on the recent remarkable results of Dufour and
Prieto-Rumeau, we deduce that for an absorbing MDP with a given initial state,
under a standard compactness-continuity condition, the space of occupation
measures has the same convergent sequences, when it is endowed with the weak
topology and with the weak-strong topology. We provided two examples
demonstrating that imposed condition cannot be replaced with its popular
alternative, and the above assertion does not hold for the space of marginals
of occupation measures on the state space. Moreover, the examples also clarify
some results in the previous literature.
