1. Let f: [a,b] ----> R and suppose f is integrable with respect to alpha. Prove that for any c in the real numbers, cf is integrable with respect to alpha and the integral from a to b of cf d(alpha) = c times integral from a to b of f d(alpha).
Give an example of a function f : [0,1] ----> R such that f is Riemann integrable and f is discontinuous on a dense subset of [0,1].© BrainMass Inc. brainmass.com October 10, 2019, 2:08 am ad1c9bdddf
Please see the attachment. Some more information on Tomae's function can be found ...
Riemann integrable function is modeled.