The Minkowski Inequality states that if are nonzero real numbers, then for any positive numbers the following holds:
Notice that if either or is zero, the inequality is equivalent to Hölder's Inequality.
Equivalence with the standard form
For , putting and , the symmetrical form given above becomes
Putting and , we get the form in which the Minkowski Inequality is given most often:
As the latter can be iterated, there is no loss of generality by putting .
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