I have attached part of 2 pages from Justin T. Moores dissertation. I am wondering why he says every set of size [itex] \aleph_1 [/itex] has measure zero. He is probably using some axioms that i am not familiar with. And Im not sure what the [itex] k_2 [/itex] is. He says this towards the bottom of the page. any help will be much appreciated.