The general set theory claims that there exists a set which has no members. From the point of view of R what are null sets? More specifically when we define structures such as algebras or subsets of R etc.
I am reading Measure theory and in there one is talking about the algebra of sets of all finite unions of the form $(a, b]$, $(-\infty, b]$, $(a, \infty)$, $(-\infty, \infty)$ how do you show that $\emptyset$ belongs to the family F of all unions of sets as mentioned above?
One way to look at it is to say sets of measure zero are null sets, but we have not defined what lebesgue measure is yet.