Has anyone attempted to introduce, or has data on such endeavor, Lebesgue integration before Riemann? I've seen many discussions about how the Riemann integral is obsolete and that it is presented because it appeals to intuition*, contrary to Lebesgue's theory, which is considerably harder.
As an aside, it does not have to be Lebesgue's integration theory exclusively. I've seen people advocating for the gauge integral as well, but I don't know much.
*Citation needed. I don't think I know anyone that understood the geometric appeal of the Riemann integral when meeting it for the first time.