Let be a finite and measurable function in , and let be freely chosen. Then there is a function such that
1. is continuous in ,
2. The measure of is ,
3. ,
where denotes the upper bound of the set of the values of as runs through all values of .
Let be a finite and measurable function in , and let be freely chosen. Then there is a function such that
1. is continuous in ,
2. The measure of is ,
3. ,
where denotes the upper bound of the set of the values of as runs through all values of .
Weisstein, Eric W. "Lusin's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LusinsTheorem.html