Recently I learned about Lebesgue integral as an alternative to Riemann integral when we want to integrate some classes of functions.
In the Riemann integral, in one dimesion, we can interpret it like the "area under the curve", and in higher dimension, it can be interpreted like the volume, etc.
I wonder for the functions which are Lebesgue-integrable but not Riemann-integrable, could I interpret the Lebesgue integral as "area under the curve" or "volum" ? Or should I interpret it with other meaning ?
Thank you very much for your help!