Hello,
If u is a positive measure, I need to show that any finite subset of L^1(u) is uniformly integrable, and if {fn} is a sequence in L^1(u) that converges in the L^1 metric to f in L^1(u), then {fn} is uniformly integrable.
I know that a collection of functions {f_alpha}_alpha_in_A...
I am supposed to calculate how fast an object is moving at the center of the Earth if thrown down some hole that was drilled through the earth. I am supposed to set up a dr/dv differential equation and solve it. I am supposed to use Gauss's law. I am to assume the Earth is uniformly dense...