Register to reply

Measure of the reals

by cragar
Tags: measure, reals
Share this thread:
Feb13-13, 05:12 AM
P: 2,466
I was reading a little about measure theory, and the measure of a singleton is zero.
So why couldn't we just describe the reals as an uncountable number of singletons which each have zero measure and then union all of these singletons.
Maybe the union only works for countable sets when talking about measure.
Phys.Org News Partner Mathematics news on
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Iranian is first woman to win 'Nobel Prize of maths' (Update)
Feb13-13, 07:26 AM
P: 930
You are trying to apply the principle that the measure of a disjoint union is the sum of the measures of the components, right?

How do you define the sum of an uncountable set of numbers?
Feb13-13, 07:35 AM
micromass's Avatar
P: 18,243
Literally looking 5 seconds at the wikipedia page on measure theory answers your questions:

Please do some research yourself before asking questions.

Register to reply

Related Discussions
Multiplicative groups of nonzero reals and pos. reals Linear & Abstract Algebra 0
Measure Theory-Lebesguq Measure Calculus & Beyond Homework 1
Measure Theory - The completion of R^2 under a point mass measure Calculus & Beyond Homework 1
|P(N)| = |Reals| Calculus & Beyond Homework 1
Find all reals: General Math 11