# A Continuous Functional Sending L^p Functions to L^1

Desvl at
Throughout, let $(X,\mathfrak{M},\mu)$ be a measure space where $\mu$ is positive.The questionIf $f$ is of $L^p(\mu)$, which means $\lVert f \rVert_p=\left(\int_X |f|^p d\mu\right)^{1/p}0$, there exists some $\delta>0$ such that $d_2(f(x_0),f(x)) 0$ and hence $f(x)$ is nonincreasing on $[0,\infty)$,……