Measure Theory ? ?algebra Question Seven

7)A algebra F is a non empty collection of subsets of a non empty set X satisfying the properties that (i) X must be a member of F, (ii) if A is a member of F, then the complement of A denoted by must be a member of F, (iii) if is a sequence of members of F, then their union must be a member of F.With a careful observation, the most part of this definition matches with the topology definition.Borel sets are sequence of intervals such that one is imbedded in the other and the left end points of these intervals form a monotonically increasing sequence and the right end points of the sequence of intervals form a monotonically increasing sequence. Both sequences converge to a unique limit point.In view of this, we can proceed with the proofs of the sub parts.In this case, we are considering just the real number field and constructing the sigma algebra.is the algebra over real numbers comprising class of intervals centred at the origin and spreading equal distances to left and right in the name of radius r.The only difference between Borel sets and the present algebra is Borel sets can be at