A new property equivalent to Lebesgue integrability
A new property equivalent to Lebesgue integrability
Using the generalized Riemann approach to Lebesgue integration we define a new property which is equivalent to Lebesgue integrability for measurable functions. Roughly speaking, this property says that Riemann sums for sufficiently fine partitions of sufficiently small intervals can always be made arbitrarily small. We formulate this property in such …