Ways to introduce Measure Theory

kshatriyakhiladi · New Member Offline Joined: 28 Jul 2005 Posts: 12

I'm hoping someone can help me address this query: How many different ways are there of introducing Measure Theory? I am aware of the following 3 methods, and wonder if these are it, or there are more.

1. Paul Halmos' approach using measures on rings of sets
2. Walter Rudin's approach using linear functionals
3. Daniell's approach

I hope to hear soon. Thanks!

**Posted:** Sun Sep 18, 2005 6:03 pm

liyi

Most of books in China use (1) and (maybe therefore) I feel that it is easier to understand than (2).

What is (3)?

**Posted:** Mon Sep 19, 2005 8:36 pm

Cezar Lupu

Does anyone know some good books with theory and also with exercices for Measure Theory? Wink

**Posted:** Thu Oct 06, 2005 12:35 pm

_________________
In the war, it is NOT the men, but the Man who counts. ( Napoleon Bonaparte)

blahblahblah

I like Rudin's Real and Complex Analysis.

**Posted:** Thu Oct 06, 2005 12:53 pm

jmerry

In general, any book with "Real Analysis" in the title is likely to be useful. The details will very, since there are a lot of these textbooks, but all should have measure theory.

**Posted:** Thu Oct 06, 2005 1:43 pm

Kent Merryfield

I'm partial to Wheeden and Zygmund, Measure and Integral. The approach there is to work out from the beginning the details of Lebesgue measure in $\mathbb{R}^n.$ This differs on the one hand from approaches that start with just $\mathbb{R}$ and on the other hand from approaches that start with abstract measure spaces.

The integral of a function $f: E\mapsto [0,\infty]$ where $E\subset\mathbb{R}^n$ is then defined as the $(n+1)$ -dimensional measure of the set $\{(x,y): x\in E,0\le y \le f(x)\}.$ One advantage of this is that it produces Fubini's theorem earlier and more naturally.

**Posted:** Thu Oct 06, 2005 2:13 pm