REALANALYSIS: MATH 209 MATH209A Textbook. The textbook is Gerald Folland’s Real Analysis. Reference. A very useful reference is H. L. Royden’s Real Analysis, or the 4th edition of this book written by Royden and P. Fitzpatrick. Wewill cover approximately the following material: • Preliminaries — Chapter 0 • Measures — Chapter 1 • Integration — Chapter 2 Topics include: • Properties of both abstract and Lebesgue-Stieltjes measures • Caratheodory extension process constructing a measure on a sigma-algebra from ...
REAL ANALYSIS II HOMEWORK 4 CIHANBAHRAN Folland, Chapter 5 1. If X is a normed vector space over K (= R or C), then addition and scalar multiplication are continuous from X × X and K ×X to X. Moreover, the norm is continuous from X to [0,∞); in fact, |kxk − kyk| ≤ kx − yk. Since X has a metric topology, to show that a map into X is continuous it suces to show that ...
“bevbook” — 2010/12/8 — 16:35 — page i — #1 AGuide to Advanced Real Analysis “bevbook” — 2011/2/15 — 16:16 — page ii — #2 c 2009by TheMathematicalAssociationofAmerica(Incorporated) Library of CongressCatalog CardNumber2009927192 Print Edition ISBN 978-0-88385-343-6 Electronic Edition ISBN 978-0-88385-915-5 Printed in the United States of America Current Printing (last digit): 10987654321 “bevbook” — 2010/12/8 — 16:35 — page iii — #3 TheDolcianiMathematicalExpositions NUMBERTHIRTY-SEVEN MAAGuides#2 AGuide to Advanced Real Analysis Gerald B. Folland University of Washington ® ...
Folland: Real Analysis, Chapter 1 S´ebastien Picard Problem 1.5 If M is the σ-algebra generated by E, then M is the union of the σ-algebras generated by F as F ranges over all countable subsets of E. (Hint: Show that the latter object is a σ-algebra.) Solution: Let N denote the union of the σ-algebras generated by F as F ranges over all count- able subsets of E. N = [ M(F): F&sub ...
REAL ANALYSIS II HOMEWORK 1 CIHANBAHRAN The questions are from Folland’s text. Section 3.1 1. Prove Proposition 3.1. Proposition 1. Let ν be a signed measure on (X,M). If {Ej} is an increasing sequence S in M, then ν( ∞E ) = lim ν(E ). If {E } is a decreasing sequence in M and ν(E ) 1T j j→∞ j j 1 is nite, then ν( ∞E ) ...
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