Suppose (X, S) is a measurable space, E1, . . . , En are disjoint subsets of X, and c1, . . . , cn are distinct nonzero real numbers. Prove that c1χE1 + · · · + cnχEn is an S-measurable function if and only if E1, . . . , En ∈ S.

Suppose (X, S) is a measurable space, E1, . . . , En are disjoint subsets of X, and c1, . . . , cn are distinct nonzero real numbers. Prove that c1χE1 + · · · + cnχEn is an S-measurable function if and only if E1, . . . , En ∈ S.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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