I would like to determine necessary and sufficient conditions for equality to hold in Minkowski's Inequality in [itex]L^{p}(X,\mu)[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

For [itex]1\leq p\leq \infty,[/itex] we have [itex]\forall f,g\in L^{p}(X,\mu)[/itex]

[tex]\left\{\int_X \left| f+g\right| ^{p} d\mu\right\} ^{\frac{1}{p}} \leq \left\{\int_X \left| f\right| ^{p} d\mu\right\} ^{\frac{1}{p}} + \left\{\int_X \left| g\right| ^{p} d\mu\right\} ^{\frac{1}{p}}[/tex]

here I wish to allow f and g to be complex. Any help would be nice.

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# Equality holds in Minkowski's Inequality when

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