VII. UNIFORMLY DISTRIBUTED OVER [0, 1] Let S = [0, 1]. Let F be the sigma algebra of all Borel measurable subsets of [0, 1]. We define a measure P : F - R by first specifying the measure on certain types of sets: Define P[[0, x]] = x Vx 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 Borel measurable sets A C [0, 1]. a) Compute P[(a, b] for 0