Let C0 be the class of all intervals in R, and consider the eight classes C j, j 1, ,8, each of which consists of all intervals in C0 of one type Then B (Cj), j 1, , 8 Also, if C 'j denotes the class we get from C j by considering intervals with rational with rational endpoints, then (C 'j) B, j 1,...

Since C j and C j C 0 j 1 8 it follows that C j and C j C 0 B so that it suffices to show that B C j and B C j which are implied respectively by C 0 C ...

Let C0 be the class of all intervals in R, and consider the eight classes C j,

Question:

Let C0 be the class of all intervals in R, and consider the eight classes C j, j = 1,...,8, each of which consists of all intervals in C0 of one type. Then B = σ(Cj), j = 1,..., 8. Also, if C'j denotes the class we get from C j by considering intervals with rational with rational endpoints, then σ (C'j) = B, j = 1,..., 8.