VII. UNIFORMLY DISTRIBUTED OVER [0,1] Let S = [0,1]. Let F be the sigma algebra of all Bore] measurable subsets of [0, 1]. We dene a measure P : F ) R by rst specifying the measure on certain types of sets: Dene P[[0,:I:]] = 3: V3: E [0, 1] In particular, P[{0}] = P[[0, 0]] = 0. The measure with this property is called the uniform measure over the interval [0,1]. We want to infer the value of P[A] for additional interesting Bore] measurable sets A Q [0, 1]. a) Compute P[(a,b]] for 0 S a