proof of Minkowski inequality
For the result follows immediately from the triangle inequality, so we may assume .
by the triangle inequality. Therefore we have
Set . Then , so by the Hölder inequality we have
Adding these two inequalities, dividing by the factor common to the right sides of both, and observing that by definition, we have
Finally, observe that , and the result follows as required. The proof for the integral version is analogous.
|Title||proof of Minkowski inequality|
|Date of creation||2013-03-22 12:42:14|
|Last modified on||2013-03-22 12:42:14|
|Owner||Andrea Ambrosio (7332)|
|Last modified by||Andrea Ambrosio (7332)|
|Author||Andrea Ambrosio (7332)|