6.2 Measurable Functions

Definition and properties of measurable functions, and distributions of random variables.

[toddkemp-probability]

@13:40 To be clear here: you don't need to use the Borel σ-field on the reals here, but you do need a σ-field that separates the points 0 and 1: there must be a measurable set B_0 containing 0 but not 1, and another measurable set B_1 containing 1 but not 0. You don't need anything so rich as the Borel σ-field to make that happen, but it isn't true of *every* σ-field.