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Posted on: Thursday, February 04, 2010 7:04 PM
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Subject: Math Measure Theory
| A Brief Introduction to Measure Theory and Integration Richard F. Bass Department of Mathematics University of Connecticut September 18, 1998 These notes are c 1998 by Richard Bass. They may be used for personal use or class use, but not for commercial purposes. 1. Measures. Let X be a set. We will use the notation: Ac = {x ∈ X : x ∈ A} and A − B = A ∩ B c . / Definition. An algebra or a field is a collection A of subsets of X such that (a) ∅, X ∈ A; (b) if A ∈ A, then Ac ∈ A; (c) if A1 , . . . , An ∈ A, then ∪n Ai and ∩n Ai are in A. i=1 i=1 A is a σ-algebra or σ-field if in addition (d) if A1 |
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