Comments on: Requests Thread

By: Disco

Disco — Sun, 07 Dec 2008 07:43:08 +0000

I’d love some probability theory and stochastics, which seems to encompass the suggestions by Todd and Johnathan.

I’ll throw in a curve ball from left field and add in the question of “How do sigma algebras avoid non-measurable functions, and how are they related to Von Neumann algebras?”.

By: Johan Richter

Johan Richter — Tue, 28 Oct 2008 03:21:13 +0000

I seventh Todd’s request. At least give a pointer to the litterature, I have been looking on and off since you first wrote that post but found nothing.

By: Chris

Chris — Mon, 27 Oct 2008 22:05:12 +0000

I second the requests for posts on Polish spaces.

Something on Sobolev spaces or Radon-Nikodym would be neat too.

By: D

Thu, 23 Oct 2008 06:40:37 +0000

I sixth Todd’s request!

By: notedscholar

notedscholar — Thu, 23 Oct 2008 04:31:47 +0000

Oh also…. just because all those people up there fourthed and fifthed that other idea…. doesn’t mean it’s better. “Truth is not decided by majority vote.” - James Madison I think

By: notedscholar

notedscholar — Thu, 23 Oct 2008 04:29:24 +0000

I would appreciate a post on either the irrationality of infinity or the irrationality of imaginary numbers. On the latter concept, note that the origin of the term is in a criticism of it. This is historically ironic! I don’t believe in either concept. But of course the latter, by its name, seems not to believe in itself.

By: Todd Trimble

Todd Trimble — Mon, 13 Oct 2008 12:35:47 +0000

How about getting around to explaining the “cavalcade of normality” of statistics, as involving the Gateaux derivative?

By: John Sidles

John Sidles — Mon, 13 Oct 2008 09:51:40 +0000

I would welcome the specific topic: why/how does density functional theory (DFT) work?

Or the broader topic, when can we expect the (present-day) exponential expansion of quantum simulation capability to run out of gas?

Across broad sectors of the global economy, this ongoing expansion is becoming the “other” Moore’s Law.

Can we foresee the mathematical limits to this expansion? What the main mathematical tools (informatic, geometric, algebraic, differential, etc.) that are being deployed to study these limits?

By: Walt

Walt — Sun, 12 Oct 2008 12:14:49 +0000

Requesting the topic of one of the posts I’m avoiding finishing? You’re diabolical, John.

By: Jonathan Vos Post

Jonathan Vos Post — Sun, 12 Oct 2008 06:17:37 +0000

Also, I suppose, I wonder about:

Random Probability Measures on Polish Spaces (Stochastics Monographs)

# Hardcover: 136 pages
# Publisher: CRC; 1 edition (July 25, 2002)
# Language: English
# ISBN-10: 0415273870
# ISBN-13: 978-0415273879

In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the random analog of the Prohorov theorem, which is obtained without invoking an embedding of the Polish space into a compact space. Further, the narrow topology is examined and other natural topologies on random measures are compared. In addition, it is shown that the topology of convergence in law-which relates to the “statistical equilibrium”-and the narrow topology are incompatible. A brief section on random sets on Polish spaces provides the fundamentals of this theory. In a final section, the results are applied to random dynamical systems to obtain existence results for invariant measures on compact random sets, as well as uniformity results in the individual ergodic theorem. This clear and incisive volume is useful for graduate students and researchers in mathematical analysis and its applications.

About the Author
Hans Crauel is of the Institut fur Mathematik at Technische Universitat Ilmenau in Germany.