I am lecturing out of R.Bartle, The Elements of Integration and Lebesgue Measure, for the first time. In the most recent lecture I got stuck not being able to argue an inequality on page 107. I cannot post the text here, sorry. But if anyone has the book, can you also explain how to derive the inequality in line 6:(adsbygoogle = window.adsbygoogle || []).push({});

g(t + n[itex]^{-2}[/itex]) [itex]\leq[/itex] g(t) + 2[itex]\epsilon[/itex] ?

The inequality G([itex]\psi[/itex][itex]_{n}[/itex]) [itex]\leq[/itex] g(t) + 2[itex]\epsilon[/itex] from the previous line does not seem to help much, since

G([itex]\psi[/itex][itex]_{n}[/itex]) [itex]\leq[/itex] G([itex]\varphi[/itex][itex]_{t + n^{-2}, n}[/itex])

follows from G being positive, and this is the opposite inequality of the desired.

Or what am I missing here? Thanks for any enlightenment!

Kind regards, Tommy

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# Help! Stuck in proof of Riesz Representation Theorem

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