There Are 2(c) Quasicontinuous Non-Lebesgue Measurable Functions

摘要

S. Marcus used a fat Cantor set to show that there is a quasicontinuous function from the interval [0, 1] to R that is not Lebesgue measurable. However, his article is not very well known. We give a very simple example of a quasicontinuous non-Lebesgue measurable function from [0, 1] to R and we show that there are 2(c) quasicontinuous non-Lebesgue measurable functions and 2(c) quasicontinuous Lebesgue measurable functions.