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30. Let B; be o-fields of subsets of 2 for i = 1, 2. Show that the o-field B1V B2 defined to be the smallest o-field containing both B1 and B2 is generated by sets of the form B1 n B2 where B; e B; for i = 1, 2.

30. Let B; be o-fields of subsets of 2 for i = 1, 2. Show that the o-field B1V B2 defined to be the smallest o-field containing both B1 and B2 is generated by sets of the form B1 n B2 where B; e B; for i = 1, 2.

Advanced Engineering Mathematics
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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30. Let B; be o-fields of subsets of 2 for i = 1, 2. Show that the o-field BVB2 defined to be the smallest o-field containing both B1 and B2 is generated by sets of the form B1 N B2 where B; e B; for i = 1, 2.
Transcribed Image Text:30. Let B; be o-fields of subsets of 2 for i = 1, 2. Show that the o-field BVB2 defined to be the smallest o-field containing both B1 and B2 is generated by sets of the form B1 N B2 where B; e B; for i = 1, 2.
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