I'm trying to understand what's going on in the answer to [this question](https://math.stackexchange.com/questions/4429077/what-does-an-exponent-of-a-differential-form-mean). Trying to do the computation myself, I get

\begin{align*}
\omega \land \omega &= (dx^1 \land dx^2 + dx^3 \land dx^4) \land (dx^1 \land dx^2 + dx^3 \land dx^4)\\
&= (dx^1 \land dx^2) \land (dx^3 \land dx^4) + (dx^1 \land dx^2) \land (dx^1 \land dx^2) + (dx^3 \land dx^4) \land (dx^1 \land dx^2) + (dx^3 \land dx^4) \land (dx^3 \land dx^4).

First keep in mind pointwise convergence of functions. Just imagine a simple example in $\mathbb R$. Now we want a concept like this in measure theory, except in true measure theory tradition we want to be able to permit behavior on sets of measure zero that we don't care about. Imagine a sequence of functions, like maybe $f_n(x) = (1/n)x$, converging to the zero function, except maybe for all $n, f_n(2) = 5$. So you have pointwise convergence except at a point.

To accomplish our goal, we come up with a concept of convergence of a sequence of functions "in measure", which essentially says …