This question should be shouldn't be too difficult, but I think that I am having difficulty as to understanding how to do the integration with respect to the Lebesgue measure.
Again let $X=\mathbb{R}$ and $\mu = \lambda$ be the Lebesgue measure. Find an example of two measurable functions, $f,h:\mathbb{R}\rightarrow \mathbb{R}$ with $h \in \mathcal{L}_1(\mathbb{R})$ and $f \notin \mathcal{L}(\mathbb{R}) $, such that $f(x) \leq h(x)$ for all $x \in \mathbb{R}$.
So initially, I thought that I could set $f=\frac{1}{x}$ and $h=1$, but then to integrate these with respect to the Lebesgue measure... help!