Lebl-Basic-Analysis-I · Problem 6.2.12

Sequences of Functions

Mathematics · pointwise-convergence-integral-pathology

Problem

Find sequences of Riemann integrable functions fn:[0,1]→Rf_n : [0,1] \to \mathbb{R} such that {fn}n=1∞\{f_n\}_{n=1}^\infty converges to zero pointwise, and such that a) {∫01fn}n=1∞\left\{\int_0^1 f_n\right\}_{n=1}^\infty increases without bound, b) {∫01fn}n=1∞\left\{\int_0^1 f_n\right\}_{n=1}^\infty is the sequence −1,1,−1,1,−1,1,…-1, 1, -1, 1, -1, 1, \ldots

Related theory

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