Every infinite compact group can have a non-measurable subgroup (Q306140)

The authors prove the statement in the title: in a model of ZFC where the real line has a subset of cardinality less than \(\mathfrak{c}\) that is not Lebesgue measurable (does not have the Baire property) every compact group has a subgroup that is not Haar measurable (does not have the Baire property). As the authors note `most' cases were settled in the literature; the assumption about subsets of the real line is used to deal with the remaining case, that of compact metric profinite groups.