Measure theory ends and probability begins with the definition of independence. We begin with what we hope is a familiar definition and then work our way up to a definition that is appropriate for our current setting.

Two events *A* and *B* are **independent** if *P(A ∩ B*) *= P(A)P(B*).

Two random variables *X* and *Y* are **independent** if for all *C, D ∈ ,*

that is, the events *A = {X ∈ C}* and *B = {Y ∈ D}* are independent.

Two σ-fields and are **independent** if for all *A ∈ * and *B ∈ * the events A and *B* are independent.

As the ...

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