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July 12th, 2011, 06:29 AM  #1 
Newbie Joined: Jul 2011 Posts: 2 Thanks: 0  Lebesgue Spaces in economics
So I am reading a quantifiable finance text book for fun (my other hobbies include basketball and running) and I have come across L spaces. Now I realize this book is over my head but its enjoyable so I will continue reading. It seems to me Lebesgue profitability spaces set of points corresponding to moments (i.e. L1>E(X) L2>Var(x) etc.) (Yes I looked up the more mathematical definition but this way I can place it in economics) But I cannot conceptualize L0 or L(infinity) probability space and the set of points they would encompass. Thanks, Cameron PS The textbook uses something like L0(omega,F,P) so I am really wondering in that context. I get in the rigourous mathamatical sense the both L0 and L(infinity) are limits but I am concerned and that L0 is not really rigorously defined but again I am only concerned about how they are used in a financial way although drawing parallels between the math and the finance would be nice. 
July 12th, 2011, 12:42 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,710 Thanks: 675  Re: Lebesgue Spaces in economics
Lebesgue spaces are usually defined in the range (1,?), where L? means essentially bounded. I've never come across L spaces for p < 1. Note that probability spaces are a subset, since in general, the total integral doesn't have to be 1, nor does the integrand have to be nonnegative. 
July 13th, 2011, 07:57 AM  #3 
Newbie Joined: Jul 2011 Posts: 2 Thanks: 0  Re: Lebesgue Spaces in economics
L0 is not a legitimate L space because it doesn't satisfy the triangle inequality but I think they use the same formula integral(abs(x)^p)ds to define the space I just don't understand what the role of the L0 subspace is for economics what does that set (as well as L(infinity)) play for economics.

July 13th, 2011, 03:17 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,710 Thanks: 675  Re: Lebesgue Spaces in economics
I have no idea what the application of any Lp space is to economics.

July 14th, 2011, 10:27 AM  #5  
Member Joined: Sep 2010 Posts: 63 Thanks: 0  Re: Lebesgue Spaces in economics Quote:
Quote:
 
July 14th, 2011, 01:21 PM  #6  
Global Moderator Joined: May 2007 Posts: 6,710 Thanks: 675  Re: Lebesgue Spaces in economics Quote:
 

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