1.7 Show that the Borel sets of R = ({(, x]| x R}). Hint:...

1.7 Show that the Borel sets of R ℬ = σ ({(−∞, x]| x ∈ R}).

Hint: show that the generating set is the same, that is, show that any set of the form (−∞, x] can be written as countable union (or intersection) of open intervals, and, vice versa, that any open interval in R can be written as a countable union (or intersection) of sets of the form (−∞, x].