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- Jun 22, 2012

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I need help with the proof of Result 2.7 ...

Result 2.7 and its proof read as follows:

In the above proof by Axler we read the following:

" ... ... Thus

... $\mid t + A \mid \leq \sum_{ k = 1 }^{ \infty } l ( t + I_k ) = \sum_{ k = 1 }^{ \infty } l ( I_k )$

Taking the infimum of the last term over all sequences $I_1, I_2, ... $ of open intervals whose union contains $A$, we have $\mid t + A \mid \leq \mid A \mid$. ... ..."

Can someone please explain exactly how/why taking the infimum of the last term over all sequences $I_1, I_2, ... $ of open intervals whose union contains $A$, we have $\mid t + A \mid \leq \mid A \mid$ ... ?...

Peter