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.

Set A that contains all its accumulation points is

The complement of an open ball is

A set is called countable if it is

The closure of a set A is

Every Borel set is

The interior of a closed set is

Let A and B be two sets. The symmetric difference A Δ B is defined as

A set A⊆R is compact if it is

A set B⊆R is said to be Lebesgue measurable if it can be

Let A be a measurable set. The measure of the complement of A is

A function f: R→R is said to be Lebesgue integrable if

Let f be a nonnegative measurable function on E. Then $$\int_Ef=0$$ if and only if

The closure of an open set is

A function f: R→R is said to be measurable if

Let A be a set in R. If A is both closed and bounded, then A is

For any measurable set A, the measure of A is

If a function f: R→R is Lebesgue integrable, then

  A function f: R→R is said to be absolutely integrable if

   If a set A is Lebesgue measurable, then its complement

The intersection of a measurable set and a Borel set is

Let A={a,b,c,d} and B={4,5,6}. Which of the following sets are functions with domain A and codomain B?

A function g: R→R is said to be uniformly continuous if