## What does it mean for a function to be integrable?

## What are the non-integrable functions of rational numbers?

- These are non-integrable.
**Functions that**have discontinuities of positive measure can not**be**Riemann**integrated**, for instance the characteristic function of the rational numbers on the unit interval. However, a more general notion of integral, the Lebesque integral, includes this function and many other**that**can not**be**Riemann**integrated**.

## Can funfunctions be Riemann integrated?

**Functions that**have discontinuities of positive measure can not**be**Riemann**integrated**, for instance the characteristic function of the rational numbers on the unit interval. However, a more general notion of integral, the Lebesque integral, includes this function and many other**that**can not**be**Riemann**integrated**.

## Are all integrable functions analytic functions?

- Since analytic
**functions**are very "nice" and the only requirement for integrability is**that**the function**be**bounded and have discontinuities only on a set of measure 0, jumping form integrable to analytic leaves out "almost all" integrable**functions**! What function are you talking about? And what do you mean by "expanding it over infinite terms"?

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