Let $(\Omega,\mathcal F,\mu)$ be a [measure space](/page/Measure%20Space), let $\mathbb K$ be either $\mathbb R$ or $\mathbb C$, and let $1<p<\infty$. Then the normed space $L^p(\Omega,\mathcal F,\mu;\mathbb K)$ is strictly convex: for all $f,g\in L^p(\Omega,\mathcal F,\mu;\mathbb K)$ satisfying