Compare the definition of with the definition of the topological boundary which can be written as
Hence one clearly has .
Notice that the essential boundary does not depend on the Lebesgue representative of the set , in the sense that if then . For example if is the set of points with rational coordinates, one has while .
Nevertheless one can easily prove that is always a closed set (in the usual sense).
|Date of creation||2013-03-22 15:01:54|
|Last modified on||2013-03-22 15:01:54|
|Last modified by||paolini (1187)|