## Absolute Continuity of Lebesgue Integral

The following is a wonderful property of the Lebesgue Integral, also known as absolute continuity of Lebesgue Integral. Basically, it means that whenever the domain of integration has small enough measure, then the integral will be arbitrarily small. Suppose is integrable. Given , there exists such that for all measurable sets with , . Proof: … Continue reading “Absolute Continuity of Lebesgue Integral”