Lusin’s Theorem and Egorov’s Theorem are the second and third of Littlewood’s famous Three Principles. There are many variations and generalisations, the most basic of which I think are found in Royden’s book. Lusin’s Theorem: Informally, “every measurable function is nearly continuous.” (Royden) Let be a real-valued measurable function on . Then for each , […]

via Lusin’s Theorem and Egorov’s Theorem — Singapore Maths Tuition

Advertisements