# 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.

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#### 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 in this solution.