Real Analyis question 3.3 dealing with measures. Please explain, thankyou in advance. Measure: non-negative set function on a o - algebra A of subsets of some space X.Properties:1) μ (φ) - 02) If A; E A and A¡ N A; = Ø; i j, for i, j E N= µ(U, A;) = E, µ(A;)...ountable additivityi=13.3) Let X be an uncountable set and let A be the collection of subsets A of X such that either A or A°is countable. Define µ(A) = 0 if A is countable and µ(A) = 1 if A is uncountable. Prove that u isa measure.

In order to prove that f is a measure, We have to show it satisfies three properties: i. f(∅)=0 ii.…

3.3) Let X be an uncountable set and let A be the collection of subsets A of X such that either A or Aº is countable. Define µ(A) = 0 if A is countable and µ(A) = 1 if A is uncountable. Prove that u is a measure.

3.3) Let X be an uncountable set and let A be the collection of subsets A of X such that either A or Aº is countable. Define µ(A) = 0 if A is countable and µ(A) = 1 if A is uncountable. Prove that u is a measure.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.4: Linear Programming

Problem 7E

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Real Analyis question 3.3 dealing with measures. Please explain, thankyou in advance.

Measure: non-negative set function on a o - algebra A of subsets of some space X.
Properties:
1) μ (φ) - 0
2) If A; E A and A¡ N A; = Ø; i j, for i, j E N
= µ(U, A;) = E, µ(A;)...ountable additivity
i=1
3.3) Let X be an uncountable set and let A be the collection of subsets A of X such that either A or A°
is countable. Define µ(A) = 0 if A is countable and µ(A) = 1 if A is uncountable. Prove that u is
a measure.

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