They talked about the "gravitational model" of economics, that the amount of trade between two economies is proportional to the product of the size of the economies each raised to some power, divided by some power of the distance between them. They showed a best fit of the 5 parameters to under a dozen data points and it looked rather awful. (I am not sure how well defined those variables are). Without any theoretical justification it seemed like a model stolen at random from physics that didn't fit well.
I've also read a published economic paper written in terms of measure theory, where it was clear the author did not understand measure theory at all. The ideas were misapplied to a simple problem in a way that made it sound very difficult. Admittedly this is partly the fault of mathematicans who teach measure theory as statistics; while you can use that model it makes things very complicated and you almost surely don't need to deal with infinities in most real problems, let alone non-measurable sets.
This arm of economics trying to ride the coattails of prestige worn by maths and physics is void of meaning.