# Step functions are dense in the intergrable functions

I am trying to show that the set of step functions $X=\{\mbox{step functions} \ I\rightarrow\mathbb{C}\}$ are dense in the set of $Y=\{\mbox{intergrable functions}\ I\rightarrow\mathbb{C}\}$ with respect to the $||.||_2$ norm.

So I need to exibit a sequence of step functions that converge to any intergable function in $||.||_2$ but I am unsure how to do this, although I can see that this makes sense conceptually.

When I say integrable I am meaning Riemann intergabilty not Lesbeuge integrable.

Thanks for any help.

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Can you use that Lebesgue integrable implies Riemann integrable, for finite integrals? Besides, what is $I$? –  newbie May 24 at 21:28
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