Lebl-Basic-Analysis-I · Problem 6.2.9

Sequences of Functions

Mathematics · l1-norm-pointwise-convergence

Problem

Find a sequence {fn}n=1∞\{f_n\}_{n=1}^\infty of Riemann integrable functions on [0,1][0,1] converging pointwise to 00, but such that lim⁡n→∞∥fn∥L1\displaystyle\lim_{n\to\infty} \|f_n\|_{L^1} does not exist (is ∞\infty), where ∥f∥L1:=∫01∣f(x)∣ dx\|f\|_{L^1} \mathrel{:=} \displaystyle\int_0^1 |f(x)|\, dx.

Related theory

Browse the problem library