8.
What does it mean to say that a collection of sets C covers
a set E of real numbers.
9.
How is the notion of ’closed set’ defined??
10.
What does it mean to say a sequence of measurable functions
<f
n
> converges to a function f in measure?
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Autumn, 1997
Page 3 of 4
11.
Let E be a nonempty subset of
, and suppose that
f:E
→
is a function.
What does it mean to say f is continuous
at a point x
ε
E?
?
12.
Suppose that <f
n
> is a sequence of realvalued functions
defined on a nonempty set E and f is a realvalued function
defined on E.
What does it mean to say the sequence <f
n
>
converges pointwise to f on E ??
13.
Suppose that <f
n
> is a sequence of realvalued functions
defined on a nonempty set E and f is a realvalued function
defined on E.
What does it mean to say the sequence <f
n
>
converges uniformly to f on E ??
14.
Suppose that f:E
→
is a function with E
⊂
.
What does it
mean to say f is uniformly continuous on E ??
15.
How is the Lebesgue outer measure of a subset E of the real
MAA5616/FINAL EXAM/PART B
Autumn, 1997
Page 4 of 4
16.
How do we define the measurability of a subset E of the real
line?
17.
Suppose that A is a subset of the real line.
What does it
mean to say a function f:A
→
is measurable??
18.
Let f:[a,b]
→
be a function.
What does it mean to say f
is of bounded variation on [a,b] ??
19.
What does it mean to say something is true almost
everywhere??
20.
Let f:[a,b]
→
be a function.
What does it mean to say f
is absolutely continuous on [a,b] ??
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 Spring '13
 Ritterd
 Continuous function, Limit of a sequence, Topological space

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