Define the function Hm : [0, 00) by 2 if me A 1 if m¢ A Hm (A) = then Hm is not a measure. b. Hm is a measure and Hm({m, p}\{n,p}) = 1. Hm is a measure and Hm({m, p}\{n,p}) = 2 a. c. d. None of these. O a b O d

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2:32 O O M •
Define the function um :
O 53% E
[0, 00) by
2 if mEА
1 if m¢ A
Hm (A) =
, then
Hm is not a measure.
b.
а.
is a measure and Hm({m, p}\{n,p}) = 1.
Hm is a measure and um ({m, p}\{n,p}) = 2
d. None of these.
с.
a
b
Q Let (X, B(R), µ) be a Borel measure space.
Suppose that {A, = [2n-1 3n+1]}, be a family of elements of B(R).
Then u(U +1,
n=1
4n-11) equals
a.0
b.1
c.3
d.4
a
b
O d
Q.Let g : [1,4] +R be continuous function.
Define G(x) = * g(t)dt. Then
II
Transcribed Image Text:2:32 O O M • Define the function um : O 53% E [0, 00) by 2 if mEА 1 if m¢ A Hm (A) = , then Hm is not a measure. b. а. is a measure and Hm({m, p}\{n,p}) = 1. Hm is a measure and um ({m, p}\{n,p}) = 2 d. None of these. с. a b Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [2n-1 3n+1]}, be a family of elements of B(R). Then u(U +1, n=1 4n-11) equals a.0 b.1 c.3 d.4 a b O d Q.Let g : [1,4] +R be continuous function. Define G(x) = * g(t)dt. Then II
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