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Unit 9: Measure Spaces

9.4 Review Questions Notes

1. Let  be a -algebra of subsets of a set X and let Y be an arbitrary subset of X. Let
 = {A Y : A }. Show that is a -algebra of subsets of Y.

2. Let (X, , ) be a measure space. Show that for any E , E  we have the equality:
1 2
(E E ) + (E E ) = (E ) + (E ).
1 2 1 2 1 2
9.5 Further Readings

Books Paul Halmos, (1950). Measure Theory. Van Nostrand and Co.
Bogachev, V.I. (2007), Measure Theory, Berlin : Springer

Online links planetmath.org/measurable space.html
mathworld.wolfram.com > Calculus and Analysis > Measure Theory

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