Measure, Integration & Real Analysis · Problem 2E.3

Integration — Sheldon Axler

Mathematics — Measure Theory · pointwise-limit-unbounded

Problem

Give an example of a sequence of continuous functions

f_1, f_2, \ldots

from

[0,1]

\mathbf{R}

that converges pointwise to a function

f: [0,1] \to \mathbf{R}

that is not a bounded function.