Talk:Product measure
From Wikipedia, the free encyclopedia
Is the uniqueness of product measure guarantee only if in cases that both (X1,Σ1,μ1) and (X2,Σ2,μ2) are σ-finite? -- Jung dalglish 16:20, 8 February 2006 (UTC)
You aer right. A counterexample to the fubini theorem where one of the measures is not sigma finite is, for example, borel measure on [0, 1] times the counting measure on [0,1]. What is the measure of the diagonal set {(x,x): x \in [0, 1]}? The repeated integrals are unequal, but how do we define its measure? What do we say in this case?
