Measure Set Theory

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

This preview shows pages 1–7. Sign up to view the full content.

Outline Defnition A Brief Overview of Measure Theory Charles B. Moss August 27, 2010 Charles B. Moss A BrieF Overview oF Measure Theory

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Outline Defnition Defnition Charles B. Moss A BrieF Overview oF Measure Theory
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Outline Defnition 1 x 2 x [) Figure: Borel Field on the Real Number Line Charles B. Moss A BrieF Overview oF Measure Theory
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Outline Defnition I
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 12

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online