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.