## models for Lebesgue measure

Which, if any, of the following steps is false?

If (ZF + "there exist an inaccessible cardinal"), then there is a model satisfying "there exists an countably additive extension of Lebesgue measure on all sets of reals" , hence satisfying "the cardinality of the continuum is real valued measurable", hence satisfying "the cardinality of the continuum is weakly Mahlo."

Put together, If (ZF + "there exist an inaccessible cardinal"), then there is a model satisfying "the cardinality of the continuum is weakly Mahlo."

I feel there is something I am not doing right here.