Here is the exercise: I have some questions:
Is this correct when k starts with 1?, the Taylor series with e starts with 0? But does the zero disappear in some way?, I can not see how.
I know that if the $\sigma$-algebra is the sigma-algebra created by the Borel sigma algebra, then all continuous functions are measurable, so the functions we would look at are measureable. If we are only given that it is the Lebesgue-measure, do we know what the sigma-algebra is? And so do we know that these functions are measurable?, so that their integral is defined?