Real analysis-Quiz II

Let  A={x,y,z,w} and B={1,2,3} . Which of the following sets are functions with domain A and codomain B?

The set of integers Z is

  Let f: R→R and let

 1) {x∊ R: f(x)> a} is measurable for all a∊ R

2) {x∊ R: f(x)= a} is measurable for all a∊ R

Then

Let the nonnegative function f be integrable over E. Then

  There exists a set of positive measure whose every subset is measurable.

   Outer measure is finite additive.

If a function g: R→R is measurable, then the set

{x∊ R: g(x) < b} is measurable for all b∊ R.

The intersection of two measurable sets is

Let C be a countable collection of measurable sets. Then the union

of all sets from C is

A singleton set {a}  is a measurable set with a positive measure.