Difference between revisions of "MAT5213"

Revision as of 13:10, 12 March 2023

Introduction to abstract measure theory and integration.

Week	Topic	Sections from Rudin's Real and Complex Analysis	Prerequisites
1	Abstract integration	Chapter 1	Real Analysis I.
2-3	Positive Borel measures	Chapter 2
4-5	Lp spaces	Chapter 3
7-9	Hilbert spaces	Chapter 4
10-12	[[Complex measures]	Chapter 5
13-14	The Radon-Nikodym theorem and its consequences	Chapter 5
15-16	Product spaces and Fubini's theorem	Chapter 6

@@ Line 3: / Line 3: @@
 ==Topics List==
 {| class="wikitable sortable"
-! Week !! Topic !! Sections from Royden !! Prerequisites
+! Week !! Topic !! Sections from Rudin's Real and Complex Analysis !! Prerequisites
 |-
 |  1
-|| [[Review of the field and completeness axions]]
+|| [[Abstract integration]]
-|| 1.1-1.3
+|| Chapter 1
-|| Undergraduate real analysis.
+|| Real Analysis I.
 |-
 |  2-3
-|| [[Topology of the real line]]
+|| [[Positive Borel measures]]
-|| 1.4-1.6
+|| Chapter 2
 ||
 |-
 |  4-5
-|| [[Lebesgue measurable sets]]
+|| [[Lp spaces]]
-|| 2.1-2.7
+|| Chapter 3
 ||
 |-
 |  7-9
-|| [[Lebesgue measurable sets]]
+|| [[Hilbert spaces]]
-|| 2.1-2.7
+|| Chapter 4
 ||
 |-
 |  10-12
-|| [[Lebesgue integration]]
+|| [[Complex measures]
-|| 4.1-4.6
+|| Chapter 5
+||
+|-
+|  13-14
+|| [[The Radon-Nikodym theorem and its consequences]]
+|| Chapter 5
 ||
+|-
+|  15-16
+|| [[Product spaces and Fubini's theorem]]
+|| Chapter 6
+||
 |}