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- I need help in order to construct and express a valid, convincing, formal and rigorous proof to Carothers Proposition 16.2 (i) ...

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 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

========================================================================================================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:

Hope that helps ...

Peter

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 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

========================================================================================================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:

Hope that helps ...

Peter