Talk:Radon measure

message: In the article, the Radon distance is defined as a supremum of integrals of bounded continuous functions. 
However, if the measure m1 is not finite and if the measure m2 is the zero measure, we could take f
to be the constant function equal to 1 and then the distance of m1 and m2 is m1(X) which is plus infinity. This is not suitable for a metric! Therefore, this part of the article needs to be corrected (e.g. by considering only finite Radon measures).
ASlateff 128.131.37.74 13:18, 11 June 2007 (UTC)
thread_title:  Radon distance - a metric? 

message: The section when Integration is defined is confusing. I do not understand what the vectorspace F has to do with anything.   —Preceding unsigned comment added by MathHisSci (talk • contribs) 17:02, 24 January 2010 (UTC)
replies: text: Recent edits clarify things, thank you. MathHisSci (talk) 21:34, 6 February 2010 (UTC)
thread_title: Integration

message: Note for an expert in the field: In the Example section the second example of those which are not Radon measures is incomplete and is in error.  Somebody needs to fix it. HowiAuckland (talk) 20:36, 5 August 2010 (UTC)
replies: text: I think the correct definition is "any set which contains an uncountable closed subset of the open interval [1,omega)" (i.e. the final point is not required and has measure 0). I need to think, though, before correcting the article, if with this definition the claim is correct.--132.76.81.190 (talk) 15:01, 6 June 2019 (UTC)
thread_title:  error in Examples 

message: The section titled Definitions begins with this statement:
"Let m be a measure on the σ-algebra of Borel sets of a Hausdorff topological space X."
As long as this section is defining what a Radon measure is, it should do this carefully.    But the word "measure" without qualification could mean a finitely-additive one or countably-additive one; one which takes values in the nonnegative reals, in the unrestricted reals, in the complexes, or in one of these number systems extended to include infinity.
Some intended properties of the "measure" here can be guessed from context . But this is an encyclopedia, not a guessing game. Exactly what kind of measure is intended here should be stated explicitly.
ALSO: The definition of "outer regular" may be quite important to include in this article (I don't know), but it should not be defined in the middle of the definition of Radon measure — since that definition does not depend on the definition of "outer regular".  (The definition of "outer regular" can be placed after the definition of Radon measure, if it is needed.)Daqu (talk) 19:19, 16 October 2014 (UTC)
thread_title:  Problem with Definition(s) 

message: this seems to be all the rage by the so-called mathematicians in "mathematical finance" (the biggest joke there is).
i've demonstrated on previous occasions that the values purported to be "measurements" in financial mathematics are not measures at all.
this stems from the fact that no "asset" (stock, bond, whatever) can be modeled by the laws of nature as a function of time.
the fact that user:Limit-theorem is citing a financial mathematics book to "add" an unproven property is unacceptable. 
the definition was fine before, and he seems to think that mathematical finance people know more than people specialising in mathematical analysis.
i am not disputing the validity or potential usefulness of this measure, but the addition by user:Limit-theorem adds nothing. 
in fact, it's almost as if he's trying to deliberately downplay the importance and central aspect of the Lebesgue measure. 
i hate to keep bringing this up, but if renowned pure mathematician Sir Andrew Wiles has called out the field http://www.ibtimes.co.uk/andrew-wiles-maths-oxford-university-bankers-times-511492 (to which no sufficient answer has been provided), then that is telling about these individuals' abuse of mathematical tools.
STOP IT 174.3.155.181 (talk) 23:48, 26 April 2016 (UTC)
thread_title:  insufficient source cited by [[user:Limit-theorem]] 

message: Regardless of what you think about the levels of rigor in financial mathematics (as in the argument directly above this), I am very skeptical of mentioning applications to financial mathematics in the head paragraph, particularly with that blurb as short as it currently is. --Dylan Thurston (talk) 18:51, 11 July 2016 (UTC)
replies: text: Agree. Will remove. The intro requires some more sensible motivation that should be provided, though. Stca74 (talk) 12:02, 27 November 2016 (UTC)
thread_title:  Why is financial mathematics in the intro? 

message: The head section says that a Radon measure needs to be only inner regular, whereas the section Definitions requires both inner regular and outer regular. Clearly one or the other needs to change. I believe Folland requires both inner and outer regular, though I don't have the book with me right now. Minimal Counterexample (talk) 20:37, 10 May 2018 (UTC)
thread_title:  Conflicting definitions 

message: The section Radon measures on locally compact spaces contains two references that do not parse properly.
I hope someone can fix this. 
There is no reason for an editor to leave the article in such a state, since failed parsings are quite obvious from their red text if the edit is previewed before it is published. 2601:200:C000:1A0:3932:3D49:97C7:A86A (talk) 19:06, 21 September 2021 (UTC)
thread_title:  Reference problem