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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
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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