sinc is not
The main results used in the proof will be that and the dominated convergence theorem.
Let and suppose it’s Lebesgue integrable in .
Consider the intervals and .
in each , .
Suppose is integrable in . Then by the dominated convergence theorem .
But and we get the contradiction .
So cannot be integrable in . This implies that cannot be integrable in and since a function is integrable in a set iff its absolute value is
|Title||sinc is not|
|Date of creation||2013-03-22 15:44:32|
|Last modified on||2013-03-22 15:44:32|
|Last modified by||cvalente (11260)|