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We study maximal orthogonal families of Borel probability measures on 2 ω (abbreviated m.o. families) and show that there are generic extensions of the constructible universe L in which each of the following holds: (1) There is a ∆ 1 3 -definable well order of the reals, there is a Π 1 2 -definable m.o. family, there are no Σ 1 2 -definable m.o. families and b = c = ω 3 (in fact any reasonable value of c will do). (2) There is a ∆ 1 3 -definable well order of the reals, there is a Π 1 2doi:10.4115/jla.v4i0.153 fatcat:psojicyqhvdxdjnmw665cg3k7a