Oh yeah, definitely reasonable. I'm a statistician by trade, so if I see R^n, I want to put a multivariate normal measure on it, which means hyperspheres. Hyp

Oh yeah, definitely reasonable. I'm a statistician by trade, so if I see R^n, I want to put a multivariate normal measure on it, which means hyperspheres. Hypercubes are cool too. Just as long as we don't treat the limit from growing the hypercube to cover R^n as being equivalent to a uniform measure on R^n. Unlike, say, in probabilistic number theory, where they shamelessly get away with defining the equivalent of a uniform probability measure on infinitely many integers, much to the consternation of every other kind of mathematician.