Let X be an infinite set. Define u : E = P(X) → Ř by %3D if A is finite µ(A) = 1 if A is infinite. Then show that µ is neither o-additive nor sigma-subadditive.
Let X be an infinite set. Define u : E = P(X) → Ř by %3D if A is finite µ(A) = 1 if A is infinite. Then show that µ is neither o-additive nor sigma-subadditive.
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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![Let X be an infinite set. Define µ :£= P(X) → R by
if A is finite
µ(A)
1
if A is infinite.
Then show that µ is neither o-additive nor sigma-subadditive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9ef01c0-28d9-4d34-9c78-bce15986cb6b%2Fe39c82c5-01c7-42a1-8acf-99b53538ddfd%2Fcpn43z_processed.png&w=3840&q=75)
Transcribed Image Text:Let X be an infinite set. Define µ :£= P(X) → R by
if A is finite
µ(A)
1
if A is infinite.
Then show that µ is neither o-additive nor sigma-subadditive.
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