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
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.