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Fine topology in potential theory and strict maxima of functions. (English) Zbl 0657.31009
The purpose of the present note is to prove the following Theorem: For an arbitrary Borel measurable function f: $${\mathbb{R}}^ m\to {\mathbb{R}}$$, the set M(f) is polar. - For an arbitrary function f, a similar result is established for strong fine maxima.

##### MSC:
 31B15 Potentials and capacities, extremal length and related notions in higher dimensions