## Blogs about: 245a Real Analysis

#### "Introduction to measure theory" now published — 3 comments

: My graduate text on measure theory (based on these lecture notes) is now published by the AMS as par … more →

Tags: book, math.CA, Update, Measure Theory

#### 245A, Notes 6: Outer measures, pre-measures, and product measures — 29 comments

: In this course so far, we have focused primarily on one specific example of a countably additive mea … more →

#### 245A: Problem solving strategies — 26 comments

: This is going to be a somewhat experimental post. In class, I mentioned that when solving the type o … more →

#### 245A, Notes 5: Differentiation theorems — 40 comments

: Let be a compact interval of positive length (thus ). Recall that a function is said to be different … more →

#### Covering a non-closed interval by disjoint closed intervals — 47 comments

: The following question came up in my 245A class today: Is it possible to express a non-closed interv … more →

Tags: math.GN, Intervals

#### 245A, Notes 4: Modes of convergence — 31 comments

: If one has a sequence of real numbers , it is unambiguous what it means for that sequence to converg … more →

#### 245A, Notes 3: Integration on abstract measure spaces, and the convergence theorems — 50 comments

: Thus far, we have only focused on measure and integration theory in the context of Euclidean spaces … more →

#### 245A, Notes 2: The Lebesgue integral — 77 comments

: In the previous notes, we defined the Lebesgue measure of a Lebesgue measurable set , and set out th … more →

#### 245A, Notes 1: Lebesgue measure — 103 comments

: In the prologue for this course, we recalled the classical theory of Jordan measure on Euclidean spa … more →

#### 245A, prologue: The problem of measure — 71 comments

: One of the most fundamental concepts in Euclidean geometry is that of the measure of a solid body in … more →

#### Course announcement: 245A, Real analysis — 17 comments

: In a few weeks (and more precisely, starting Friday, September 24), I will begin teaching Math 245A, … more →