Lebesgue Spaces Inclusion

• March 16th 2010, 09:29 PM
DJDorianGray
Lebesgue Spaces Inclusion
Need help with the following:

Show that $(L_p(E) \cap L_{\infty}(E)) \subset L_q$ if $1 \leq p < q < \infty$.

(I am talking about Lebesgue spaces as in here: Lp space - Wikipedia, the free encyclopedia)

Thanks!
• March 17th 2010, 06:20 AM
Focus
$\int f^q d\mu=\int f^p f^{q-p} d\mu \leq ||f^{q-p}||_\infty \int f^p d\mu$