Does there exist a strictly positive non-integrable functions f,g:[0,1]-->R such that their product fg is integrable?
Please provide an example or prove that they don't exist.
just a question i was pondering
Let f(x) = 1/2 if x is rational and be equal to 2 if x is irrational. Let g(x) = 2 if x is rational and be equal to 1/2 if x is irrational. Both f and g are not Riemann-integrable (I'm assuming this is the type of integrability you're talking about) in [0,1] since they both have an uncountable amount of discontinuities in the interval. But fg = 1, which is integrable.