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Math 318 HW #7
Due 5:00 PM Thursday, March 24
Reading:
§
17–19.
Problems:
1. Exercise 20.12.
2. Exercise 20.16.
3. We say that a sequence (
f
n
) deﬁned on a measurable set
A
⊆
R
converges in measure
to a
function
f
:
A
→
R
if
lim
n
→∞
m
{
x
∈
A
:

f
n
(
x
)

f
(
x
)
 ≥
δ
}
= 0
for all
δ >
0.
(a) Show that if (
f
n
) converges to
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Unformatted text preview: f almost everywhere on A , then it converges to f in measure (cf. Exercise 20.26). (b) Suppose ( f n ) converges in measure to f on A . Show that ( f n ) converges in measure to a function g if and only if f = g (a.e.). 4. Exercise 20.36. 1...
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This note was uploaded on 08/20/2011 for the course MATH 318 taught by Professor Staff during the Spring '08 term at Haverford.
 Spring '08
 Staff
 Math

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