Is it possible to assign improper integrals over the reals a surreal value in a consistent way? Are there any papers available on this?
Note that I am not inquiring about formalizing integration over the surreal themselves, which I realize is still a somewhat open problem. Rather, I would like to identify an integral with a number $z$ in the surreals, e.g.
$\int_{\mathbb{R}^+} x^2 dx = z, \; z\in \text{Surreals}$
with the ultimate purpose of comparing and performing algebra on the values of "classically" divergent integrals.