The Reduced Boundary
Recalling that when considering functions in BV we are really considering equivalence classes of functions, we see that changing a function on a set of measure zero gives, as far as BV is concerned, the same function. In the same way when considering Caccioppoli sets the perimeter and other properties are unchanged if we make alterations of measure zero. In other words we are really concerned with equivalence classes of Caccioppoli sets.
KeywordsEquivalence Class Hausdorff Dimension Measure Zero Isoperimetric Inequality Tangent Hyperplane
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