(i) The integral of a non-negative extended real-valued measurabele function f on R d is given by R d f (x)dx = sup g R d g(x)dx where the supremum is taken over all bounded functions 0 ≤ g ≤ f which are bounded and supported on a set of finite measure. (ii) First suppose α < −n, and define a strictly decreasing sequence x m 0. We define step functions g n as follows. Define the sets A m = B xm...
