Mathematics — Real Analysis · pointwise-convergence-integrals
Problem
Find sequences of Riemann integrable functions fn:[0,1]→R such that {fn}n=1∞ converges to zero pointwise, and such that
(a)) {∫01fn}n=1∞ increases without bound,
(b)) {∫01fn}n=1∞ is the sequence −1,1,−1,1,−1,1,…