Measure Set Theory

Measure Set Theory - Outline Denition A Brief Overview of...

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Outline Defnition A Brief Overview of Measure Theory Charles B. Moss August 27, 2010 Charles B. Moss A BrieF Overview oF Measure Theory
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Outline Defnition Defnition Charles B. Moss A BrieF Overview oF Measure Theory
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Outline Defnition Defnition I A measure is an extended real valued non-negative, and countably additive set function ( μ )deFnedonar ing( R )and such that μ ( )=0 . I Taking the ring to be points on the number line as depicted in ±igure 1 Charles B. Moss A BrieF Overview oF Measure Theory
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Outline Defnition 1 x 2 x [) Figure: Borel Field on the Real Number Line Charles B. Moss A BrieF Overview oF Measure Theory
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Outline Defnition I Assume the set mapping function from these sets of x stothe real number line μ ( { x } )= 1 2 ( x j x i ) 2 μ : X R 1 (1) I Taking a couple of examples I Looking at unit intervals E 1 =[ x 1 , x 2 )=[1 , 2) μ ( E 1 1 2 E 2 =[2 , 3) μ ( E 2 1 2 E 3 =[3 , 4) μ ( E 3 1 2 E 4 =[4 , t ) μ ( E 4 1 2 (2) Charles B. Moss A BrieF Overview oF Measure Theory
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Outline Defnition I
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Measure Set Theory - Outline Denition A Brief Overview of...

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