  We reformulate Mesiar's hypothesis [Possibility measures, integration and
fuzzy possibility measures, Fuzzy Sets and Systems 92 (1997) 191-196], which as
such was shown to be untrue by Murofushi [Two-valued possibility measures
induced by $\sigma$-finite $\sigma$-additive measures, Fuzzy Sets and Systems
126 (2002) 265-268]. We prove that a two-valued $\sigma$-maxitive measure can
be induced by a $\sigma$-additive measure under the additional condition that
it is $\sigma$-principal.
