Let $(E,\mathcal E,\mu)$ be a [measure space](/page/Measure%20Space) such that $\mu(E)<\infty$. Let $1\le p<\infty$, and let $f:E\to\mathbb R$ be an $\mathcal E$-[measurable function](/page/Measurable%20Function) such that $f\in L^\infty(E,\mathcal E,\mu)$. Then $f\in L^p(E,\mathcal E,\mu)$ and