TITLE: What are Some Tricks to Remember Fatou's Lemma?
QUESTION [102 upvotes]: For a sequence of non-negative measurable functions $f_n$, Fatou's lemma is a statement about the inequality
$$\int \liminf_{n\rightarrow \infty} f_n \mathrm{d}\mu \leq  \liminf_{n\rightarrow \infty}(\int f_n \mathrm{d} \mu)$$
or alternatively (for sequences of real functions dominated by some integrable function)
$$\limsup_{n\rightarrow \infty}(\int f_n \mathrm{d} \mu) \leq \int \limsup_{n\rightarrow \infty} f_n \mathrm{d}\mu$$
I keep forgetting the direction of these two inequalities. I know that using the concepts repeatedly is the best way to remember them. 
But I am interested about learning intuitive tricks that people use to quickly remember them. 
(For instance, to remember the direction of Jensen's inequality, I just picture a convex function and a line intersecting it.)

REPLY [8 votes]: I remember the chain of inequalities
$$\int \liminf_{n\rightarrow \infty} f_n \mathrm{d}\mu 
\leq  \liminf_{n\rightarrow \infty}\int f_n \mathrm{d} \mu
\leq  \limsup_{n\rightarrow \infty}\int f_n \mathrm{d} \mu
\leq  \int\limsup_{n\rightarrow \infty} f_n \mathrm{d} \mu
$$
the middle of which is easy to remember and the rest can be easily deduced.