\begin{equation*}Let\text{ } (X,\mathcal{A} ,\mu ) \text{ }be \text{ }a \text{ }complete\text{ } \sigma -finite\text{ } measure\text{ } space \\and \text{ }Y \text{ }be \text{ }a \text{ }separable\text{ } Banach\text{ } space\text{ } supplied \text{ }with \text{ }the \text{ }norm\text{ } \left\Vert .\right\Vert . \\For \text{ }every \text{ }p,1\leq p<\infty \text{ } let \text{ } L^{p}(X,Y,\mu ) \text{ }be \text{ }the \text{ }vector \text{ }space \text{ }of \text{ }all \text{ }equivalence \text{ }classes\\ with \text{ }the \text{ }norm \text{ }\left\Vert f\right\Vert _{p}=(\int_{X}\left\Vert f\right\Vert ^{^{^{p}}}d\mu )^{\frac{1}{p}}. \\(adsbygoogle = window.adsbygoogle || []).push({});

Question: \text{ }How \text{ }do \text{ }I \text{ }writing \text{ }elements\text{ } L^{p}(X,Y,\mu ) \text{ }mathematically?\\

Thanks

\end{equation*}

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# Equivalence classes

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