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2. Suppose that 2 = (0, 1] and let Bo denote the collection of all sets of the form (a1, bi]U (a2, ba] U.U (a, ba] where k EN is finite and 0 < a1 < b, < az < bz <...< a < br S 1. (a) Carefully verify that (i) NE Bo, (il) if A E Bo, then A e Bo, and (iii) if A, A2,... A, e Bo, then Bo.

2. Suppose that 2 = (0, 1] and let Bo denote the collection of all sets of the form (a1, bi]U (a2, ba] U.U (a, ba] where k EN is finite and 0 < a1 < b, < az < bz <...< a < br S 1. (a) Carefully verify that (i) NE Bo, (il) if A E Bo, then A e Bo, and (iii) if A, A2,... A, e Bo, then Bo.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose that SN = (0, 1] and let B, denote the collection of all sets of the form 2. (a1, b1] U (a2, b2] U..U (a, bu] where k EN is finite and 0 < aj <b1 < az < bz <...< ag < bx < 1. (a) Carefully verify that (i) NE B,, (ii) if A E Bo, then A E Bo, and (iii) if A1, A2, .... A, E Bo, then UA E B. Bo. (b) Now verify that B, is not closed under countable unions by explicitly finding events A, A.... e B, with the property that A, B. j=1
Transcribed Image Text:Suppose that SN = (0, 1] and let B, denote the collection of all sets of the form 2. (a1, b1] U (a2, b2] U..U (a, bu] where k EN is finite and 0 < aj <b1 < az < bz <...< ag < bx < 1. (a) Carefully verify that (i) NE B,, (ii) if A E Bo, then A E Bo, and (iii) if A1, A2, .... A, E Bo, then UA E B. Bo. (b) Now verify that B, is not closed under countable unions by explicitly finding events A, A.... e B, with the property that A, B. j=1
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