PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (230)
Orphanage
Unclass'd
Unproven (519)
Corrections (16)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Low Entry average rating: Medium
summable function (Definition)

A measurable function $ f : \Omega \to \mathbb{R}$ where $ (\Omega, \mathcal{A}, \mu)$ is a measure space is said to be summable or integrable if the Lebesgue integral of the absolute value of $ f$ exists and is finite,

$\displaystyle \int_{\Omega} \vert f\vert d\mu < +\infty$    

An alternative way of expressing this condition is to assert that $ f \in L^1(\Omega)$.



"summable function" is owned by ehremo. [ full author list (2) ]
(view preamble)

View style:

See Also: Lebesgue integrable

Other names:  integrable function
Keywords:  summable integrable Lebesgue
Log in to rate this entry.
(view current ratings)

Cross-references: finite, absolute value, Lebesgue integral, measure space, measurable function
There are 14 references to this entry.

This is version 4 of summable function, born on 2008-07-13, modified 2008-08-02.
Object id is 10783, canonical name is SummableFunction.
Accessed 499 times total.

Classification:
AMS MSC: 28A25 (Measure and integration :: Classical measure theory :: Integration with respect to measures and other set functions)
Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)