Let X be an arbitrary set. A be a class of subsets of X and I...
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Let X be an arbitrary set. A be a class of subsets of X and I be an extended real-valued function : A(0, +00). When is said to be countably sub-additive. (1) (ii) said to be a measure on A. (b) (i) Let (X.A.) be a measure space. Prove that, if (A) is an arbitrary sequence of sets in A, then (UA) ≤ (A₂) Let X be an arbitrary set. A be a class of subsets of X and I be an extended real-valued function : A(0, +00). When is said to be countably sub-additive. (1) (ii) said to be a measure on A. (b) (i) Let (X.A.) be a measure space. Prove that, if (A) is an arbitrary sequence of sets in A, then (UA) ≤ (A₂)
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To prove that is countably subadditive we need to show that for any countable sequence of sets Ak in ... View the full answer
Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
Posted Date:
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