# Thread: every subset of a null set is also a null set

1. ## every subset of a null set is also a null set

I want proof of this statement

"every subset of a null set is also a null set"...

Where Null set is a set whose measure is 0

2. ## Re: every subset of a null set is also a null set

One of the conditions for a measure, m, is that if $\displaystyle A\subseteq B$ then $\displaystyle m(A)\le m(B)$.

3. ## Re: every subset of a null set is also a null set

Thanks a lot

I want to ask another thing related to it that how can we prove

Phy belongs to Rn

Where Rn denotes all null subsets of algebra R

4. ## Re: every subset of a null set is also a null set

What do you mean by "Phy"?

5. ## Re: every subset of a null set is also a null set

greek work phy means null or empty...

6. ## Re: every subset of a null set is also a null set

Originally Posted by awais100
greek work phy means null or empty...
It is phi [TEX]\Phi \phi[/TEX] gives $\displaystyle \Phi~~ \phi$
That is a letter of the Greek alphabet it is not a Greek word, much less a work.

In all the treatments of measure that I have seen the fact $\displaystyle \mu(\emptyset)=0$ is part of the definition of measure.

7. ## Re: every subset of a null set is also a null set

Sorry for the typo mistake

Thanks

8. ## Re: every subset of a null set is also a null set

In any case the empty set is a subset of every set and certainly has measure 0, therefore is in Rn.