Let C R, where R is the set of all real numbers Let I be the set of all open intervals in R The Borel field on the real line is given by By definition, B 0 contains the open intervals Because a,) (, a) c and B 0 is closed under complements, it contains all intervals of the form a,), for a R Continu...

Solution Since B0 contains all open intervals it contains all intervals of the for ...

Let C = R, where R is the set of all real numbers. Let I be the

Question:

Let C = R, where R is the set of all real numbers. Let I be the set of all open intervals in R. The Borel σ-field on the real line is given by

By definition, B₀ contains the open intervals. Because [a,∞) = (−∞, a)^c and B₀ is closed under complements, it contains all intervals of the form [a,∞), for a ∈ R. Continue in this way and show that B₀ contains all the closed and half-open intervals of real numbers.