proof of Vitali’s Theorem
Consider the equivalence relation in given by
that is is obtained translating by a quantity to the right and then cutting the piece which goes beyond the point and putting it on the left, starting from .
Now notice that given there exists such that (because is a section of ) and hence there exists such that . So
So if we had and if we had .
So the only possibility is that is not Lebesgue measurable.
|Title||proof of Vitali’s Theorem|
|Date of creation||2013-03-22 13:45:50|
|Last modified on||2013-03-22 13:45:50|
|Last modified by||paolini (1187)|