MATH 574 Midterm: MATH 574 McGill Examf98

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 574
• Professor: All

Document Summary

All questions are of equal weight, each is alloted 20 marks. This exam has 7 questions and 9 pages. 1. (i) (5 points) de ne the concept - eld . (ii) (5 points) de ne the concept measure on a - eld. (iii) (5 points) let y be a subset of x. For any family m of subsets of x, denote by my the family my = {m y ; m m} of subsets of y . If m is a - eld of subsets of x, show that my is - eld on y . Then there exists a m such that b = a y . But y \b = (x\a) y my , k=1 ak) y and it follows that s (c) let bk my for k n, then there exist ak m with bk = ak y . But now we nd since (x \ a) m. k=1 bk = (s .