It’s a continuous probability measure, meaning it has no atoms, but it does assign positive probability to all cylinder sets. If you take the binary representation of reals in the [0,1] interval, P_u comes from the Lebesgue measure (a uniform distribution).
It’s a continuous probability measure, meaning it has no atoms, but it does assign positive probability to all cylinder sets. If you take the binary representation of reals in the [0,1] interval, P_u comes from the Lebesgue measure (a uniform distribution).
So the probability of a cylinder set Γ(x)={s∈B∞∣x⪯s} is 2−l(x) etc?
Yes.