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## Homework Statement

I am looking for an example of a series of funtions:

[tex]\sum g_n[/tex] on [tex]\Re[/tex]

such that:

[tex]\int_{1}^{2}\displaystyle\sum_{n=1}^{\infty}g_n(x) \, dx \neq \displaystyle\sum_{n=1}^{\infty} \, \int_{1}^{2} \, g_n(x) \, dx[/tex]

"dx" is the Lebesque measure.

**2. The attempt at a solution**

I haven't attempted a solution as I'm not sure how to approach this problem. If somebody could explain this to me or link to sample problems similar to this, I would really appreciate it.