Let be a Lebesgue integral with a measure M on the interval (a,b) so:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_{a}^{b}dMf(x)=I(a,b,M) [/tex]

We don't know or can't say what M (measure) is , however my question is if we had a trial function U(x) so we could calculate I(a,b,M) for this U without recalling to the measure,either by numerical or other methods my question is if we could obtain the form of the measure , from the value of the integral:

[tex] \int_{a}^{b}dM\mathcal U(x) [/tex] ?.

I mean, to know the lebesgue integral you should know the measure, but if you knew the exact (or approximate) value of an integral could you extract the measure from it?.

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# Defining the measure.

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