... (X, A, µ) and (Y, B, ν) are two measure spaces, i.e., A and B are σ-algebras on X and Y ,resp., and µ and ν are measures on A and B, resp. A rectangle is a set of the form A ×B, where A ∈ A andB ... Suppose A 0is a algebra, A is the smallest σ-algebra containing A 0, and M is the smallestmonotone class containing A 0. Then M = A. Proof. A σ-algebra is clearly a monotone class, so A ⊂ M. ... A; (b) if A ∈ A, then A c∈ A; (c) if A 1, . , A n∈ A, then ∪ni=1 A iand ∩ni=1 A iare in A. A is a σ-algebra or σ-field if in addition(d) if A 1, A 2, . are in A, then ∪∞i=1 A iand ∩∞i=1 A iare...