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Here is the problem statement I am currently working with:

Let $\Lambda:C[0,1]\rightarrow\mathbb{C}$, and $\Lambda f = \int_0^1 f(x)e^x\ dx$. Let $\mu$ be a the measure given by the Riesz Representation theorem. What are the locally regular sets?

I am currently looking through my textbook for theorems that may be applicable to this, but I am having little luck. I think part of my problem is that I cannot find a definition for local regularity in my notes or text. I understand that a Borel set is regular if it is both outer and inner regular, and I may have a semi-intuitive idea of what constitutes local regularity, but how is the concept formally defined?

Because I have made almost no progress, I would appreciate a small push in the right direction. Any help is appreciated.

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    What is your definition of locally regular sets?2013-07-05

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