I am in physics. I am trying to improve my understanding of differential forms & particularly, here, the wedge product. I know that the wedge product allows a more general calculation of area, but I realize now that I don't know what area is. Wiki defines area using a Jordan measure, but I don't know any measure theory. I am more than willing to shelve the question of what area is until I learn more measure theory.
However, I am hoping that someone can at least point out the minimum structure which needs to be defined on my set without measure theory. i.e. it would be nice to know what kind of space I could be finding area in.
I would a assume the space needs a metric. I want to say it should have inner product, but I am not sure.