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**"not riemann integrable" => "not lebesgue integrable"??**

Hi,

In general if a function is not Riemann integrable does this mean the function is also not Lebesgue integrable? Why or why not?

I know that if the the function is Riemann integrable then its Lebesgue integrable, but I can't find any info about non-Riemann integrable functions. Maybe I'm not thinking about this in the right way...

For example, if you wanted to show 1/x is not Lebesgue integrable it would be very convenient if all you needed to show was that the Riemann integral was infinite. Otherwise I'm not sure how to compute the Lebesgue integral...Is there a straightforward method to computing integrals of such simple functions?

Any thoughts would be appreciated!