$L^p$ and $\ell^p$ spaces

Question

I'm confused. I've read that for $1\leq p<q<\infty$ following inclusions are true:

$$\mbox{1)}\qquad \ell^p\subset\ell^q$$

$$\mbox{2)}\qquad L^q\subset L^p$$

My question is - why inclusions are opposite? Isn't $\ell^p$ a special case of $L^p$? (with counting measure)

It would be nice if somebody clarified it to me...

Answer 1

2) Is true if the base set has finite measure and 1) is true if every element is an atom.