(2 pts.) How is the Lebesgue outer measure of a subset E of
the real line defined in terms of the length of an interval l(I)?
(2 pts.) How do we define the measurability of a subset E of
the real line?
(2 pts.) Suppose that A
(2 pts.) Let E be a non-empty subset of , and suppose that
f:E is a function. What does it mean to say f is continuous at
a point x E ? [Definition! Use complete sentences.]
Suppose that <fn> is a sequence of real-valued
(2 pts.) What does it mean to say that a set U of real
numbers is open? [This is a request for the definition.]
(2 pts.) What does it mean to say that a real number x is a
point of closure of a set E of real numbers?
(2 pts.) Suppose that <xn> is an infinite sequence.
does it mean to say that <xn> is a Cauchy sequence? [Hint:
is really a request for the definition!]
(2 pts.) Complete the equation below to provide the
definition of l
MAA5616/FINAL EXAM/PART C
Page 1 of 6
[Open Book Portion in Class]
Instructions: Choose any three of the following problems to solve.
Circle the number of each problem you want graded. Given the time
constraints, write up your solutions
MAA5616/FINAL EXAM/PART B
Page 1 of 4
[In Class Closed Book Portion]
Instructions: Using complete sentences and appropriate notation,
either define the given term or expression, or answer the given
Suppose that <xn> is an i
MAA5616/FINAL EXAM/PART A
[Take Home Section]
Read Chapter 5 of your text, Roydens, Real Analysis, third
edition, and solve and write up the problems out of Sections 5-1,
5-2, 5-3, and 5-4 which have been assigned to you in the