Explore BrainMass

Difference Between Measurable Functions

Please see the attached file for the fully formatted problems.

Given: and and is measurable and is a null set.

1) is zero except on the null set, true of false?

2) where is a null set, true or false?

I have been told that both 1 and 2 are true, but I don't understand why. Since the set {x: f(x)=g(x)} is null, it seems to me that d(x) should be only be zero on the null set, whereas apparently it is zero everywhere EXCEPT the null set. It may be a typo, but more likely I'm just not seeing something incredibly obvious. Also, I'm told that the truth of 1 implies 2, but again I don't see why.


Solution Preview

Both 1 and 2 are false.

1. False.
Since the set {x: f(x)=g(x)} is a null set and the null set is the empty set. It means that for any x in E,
f(x) is not ...

Solution Summary

Measurable functions are investigated.