Redirected from Holder inequality
By choosing S to be the set {1,...,n} with the counting measure, we obtain as a special case the inequality
valid for all real (or complex) numbers x1,...,xn, y1,...,yn. By choosing S to be the natural numbers with the counting measure, one obtains a similiar inequality for infinite series.
For p = q = 2, we get the Cauchy-Schwarz inequality.
Hölder's inequality is used to prove the triangle inequality in the space Lp and also to establish that Lp is dual to Lq.
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