Originally Posted by

**surjective** Hey,

Here is what I have done with $\displaystyle f+g$:

$\displaystyle \left( \int_{]-\infty,\infty[} \vert\chi_{[0,1[}+\chi_{[1,2[} \vert^{p} dx \right)^{\frac{1}{p}}$ =

$\displaystyle \left( \int_{[0,1]} \vert\chi_{[0,1[}+\chi_{[1,2[} \vert^{p} dx \right)^{\frac{1}{p}}$ + $\displaystyle \left( \int_{[0,1]^{c}} \vert\chi_{[0,1]^{c}}+\chi_{[1,2]^{c}} \vert^{p} dx \right)^{\frac{1}{p}}$ =

$\displaystyle \left( \int_{[0,1]} \vert 1+1 \vert^{p} dx \right)^{\frac{1}{p}}$ + $\displaystyle \left( \int_{[0,1]^{c}} \vert 0+0 \vert^{p} dx \right)^{\frac{1}{p}}$ =