We study maximal orthogonal families of Borel probability measures on 2 (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 ∆3 -definable well-ordering of the reals, there is a Π 1 2 -definable m.o. family, there are no Σ2 -definable m.o. families and b = c = ω3 (in fact any reasonable value ...