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Lebesgue Outer Measure ... Carothers, Proposition 16.2 (i) ...

Peter

Well-known member
MHB Site Helper
Jun 22, 2012
2,918
I am reading N. L. Carothers' book: "Real Analysis". ... ...

I am focused on Chapter 16: Lebesgue Measure ... ...

I need help with the proof of Proposition 16.2 part (i) ...

Proposition 16.2 and its proof read as follows:



Carothers - Proposition 16.2 ... .png



Carothers does not prove Proposition 16.2 (i) above ...

Although it seems intuitively obvious, I am unable to construct and express a valid, convincing, formal and rigorous proof of the result ...

Can someone please demonstrate a formal and rigorous proof of Proposition 16.2 (i) above ...

Peter



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It may help readers of the above post to have access to Carothers introduction to Lebesgue outer measure ... so I am providing the same as follows:



Carothers - Proposition 16.1 ... .png


Hope that helps ...

Peter
 
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