Positive Measure: Measure of Sets with Positive Function Value

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Homework Statement


Suppose that if k is a measurable function and {x : k(x) > 0} has a positive measure, then {x : k(x) >= p} has positive measure for some p > 0

Homework Equations


Lebesgue measure

The Attempt at a Solution


What is positive measure? is it just another word for measurable? Can I have some hint on how to attack this problem?

Thank you.
 
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bump!

i just need hint.

thanks
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
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