Mathematics Homework Solutions
Problem
#160542

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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is a null set.

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

is a null set, true or false?

Solution Summary

Measurable functions are investigated.

Solution
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Yupei Xiong, PhD - 4.8/5
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