Suppose that M is a o-algebra over R, and µ : M → [0, ∞] is a finitely additive function such that the following hold: If {A;} C M is an increasing nested sequence, then µ(U,A;) = lim μ ( A ). µ(0) = 0. Show that u is a measure.
Suppose that M is a o-algebra over R, and µ : M → [0, ∞] is a finitely additive function such that the following hold: If {A;} C M is an increasing nested sequence, then µ(U,A;) = lim μ ( A ). µ(0) = 0. Show that u is a measure.
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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![Suppose that M is a o-algebra over R, and µ : M → [0, 0] is a finitely
additive function such that the following hold:
If {A;} CM is an increasing nested sequence, then µ(U,A;)
lim μ ( A ).
n 00
µ(Ø) = 0.
Show that u is a measure.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c3ce0fd-4090-405c-80f4-99d74f0446d4%2Fd31e51fa-8728-4f31-b528-6f550912f337%2Fp39ct4j_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that M is a o-algebra over R, and µ : M → [0, 0] is a finitely
additive function such that the following hold:
If {A;} CM is an increasing nested sequence, then µ(U,A;)
lim μ ( A ).
n 00
µ(Ø) = 0.
Show that u is a measure.
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