Goklayeh
Oct5-10, 10:58 AM
Could someone confirm or refute the following statement?
f \in L^p\left(X, \mu\right) \: \Leftrightarrow \: \int_X{\lvert fg \rvert d\mu < \infty\: \forall g \in L^q\left(X, \mu\right)
where 1<p<\infty,\: \frac{1}{p}+\frac{1}{q}=1 and (X, \mu) is a measurable space (of course, the (\Rightarrow) is trivial by Holder inequality)
Thanks in advance!
f \in L^p\left(X, \mu\right) \: \Leftrightarrow \: \int_X{\lvert fg \rvert d\mu < \infty\: \forall g \in L^q\left(X, \mu\right)
where 1<p<\infty,\: \frac{1}{p}+\frac{1}{q}=1 and (X, \mu) is a measurable space (of course, the (\Rightarrow) is trivial by Holder inequality)
Thanks in advance!