3. (a) Define lim inf→ fn and lim supno fn and explain why these functions are measur- able (b) Suppose that lim info fn = lim supno fn almost everywhere, what can you say about the existence and measurability of limno fn? (c) Define the symmetric difference A AB=(AUB) - (An B). Show that AAB= (A - B) U (B - A)

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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3. (a) Define lim infn→∞ fn and lim supno fn and explain why these functions are measur-
able
(b) Suppose that lim inf→∞ fn = lim supno fn almost everywhere, what can you say about
the existence and measurability of limn→∞ fn?
(c) Define the symmetric difference A AB= (AUB) - (An B).
Show that AA B=(A-B) U (B - A)
Transcribed Image Text:3. (a) Define lim infn→∞ fn and lim supno fn and explain why these functions are measur- able (b) Suppose that lim inf→∞ fn = lim supno fn almost everywhere, what can you say about the existence and measurability of limn→∞ fn? (c) Define the symmetric difference A AB= (AUB) - (An B). Show that AA B=(A-B) U (B - A)
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