Talk:Probability space
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| Mathematics rating: | Start Class | Top Priority | Field: Probability and statistics | ||||||||||||||||||||
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[edit] Relate
How does this relate to the concept of elementary event? - Patrick 10:20 Jan 13, 2003 (UTC)
[edit] Issues
A couple of issues:
- The article tries to explain the difference between Ω and S with some examples, but these do not really get to the heart of the matter. What is the difference, in general? Is it that the elements of S must be (tuples of) measurable quantities?
- The article notes that not all subsets of a probability space are events, but does not give an example or explain why this is so.
It would be nice if someone it it upon him- or herself to address these. Dbtfz 04:23, 19 January 2006 (UTC) Dbtfz 04:23, 19 January 2006 (UTC)
- Example 2 is so verbose that its difficult to follow. I wonder if this could be replaced with easy to understand example. Example 1 is excellent but a bit trivial
[edit] Symbol Pr
Speaking foundationally, the notation Pr() is not more precise, as it obscures the fact that P is just a function like any other, and a situation using P for Probability and some other function is being inconsistent. Jfr26 11:18, 16 April 2006 (UTC)
- P is here defined as a measure, with support on some appropriate sigma-algebra, while in my experience Pr(A) is literally shorthand for "the probability that A". Precise use of P—rather than Pr—is the goal, and speaking personally, I like Pr because it handily ties together a string of notational conventions, at the cost of one extra keystroke. More to the point, it's commonly used for the above-described shorthand purpose by mathematicians and others and so deserves some additional explanation. Ben Cairns 14:03, 27 April 2006 (UTC)
[edit] Merge
If someone can check that all of the relevant information has been moved to probability theory, we might be able to delete this page and replace it with a redirect? MisterSheik 17:12, 28 February 2007 (UTC)
- Don't merge. There are too many articles which link specifically to Probability space for the specific material here, not for that material buried in a more general treatment. Jheald 18:36, 3 March 2007 (UTC)
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- Is it a more general treatment though? Unless I'm missing something, the whole article on probability theory is just the definition of probability space. The probability axioms are really part of the definition of probability space since they're restrictions on one of the components of a "probablity space". What do you think? MisterSheik 18:56, 3 March 2007 (UTC)
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- That may be part of the problem. Probability theory should be the top-level article for the whole of the mathematics associated with probability, as distinct from Probability broadly treating the question, "what is probability?". Now the whole of the mathematics associated with probability theory is a much bigger subject than the definition of probability space, as any number of textbooks with the title "Theory of probability" indicate. Jheald 19:36, 3 March 2007 (UTC)
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- Regarding the probability axioms, I would treat them first, before introducing the full detail on probability spaces. The laws of probability apply perfectly well to probabilities of finite numbers of discrete events, and are most easily conveyed in that setting first, in terms of elementary events. Only having treated the finite case first is it useful to generalise to the full works of measure theory and countably infinite sets - which may be beyond what some readers ever need to use. Jheald 22:23, 3 March 2007 (UTC)
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[edit] Re-redirect probability measure ?
Suggest changing the redirect of probability measure to measure (mathematics), rather than here.
What do people think ? Jheald 21:29, 3 March 2007 (UTC)
- For minor things like that, it is often better to just make the change and then discuss if someone cares enough to revert it (see WP:BRD). It saves a lot of discussion for things that are truly insignificant. CMummert · talk 00:58, 4 March 2007 (UTC)
[edit] Why start class?
Why is this article start class? It seems almost done. MisterSheik 23:58, 17 June 2007 (UTC)
- The content is fine, but it could be more accessible. This does not mean it everything in the article should be understandable to everyman, but that each topic should be made as accessible as it can be. Geometry guy 00:08, 18 June 2007 (UTC)
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- I'm all for accessibility as long as it doesn't make things difficult for people that want to use the encyclopedia as a reference (as a opposed to a tutorial). That's why the examples are separated from the text. I think maybe some better examples, and an extra paragraph to the lead would do it? MisterSheik 01:41, 18 June 2007 (UTC)
- Sounds good. WP:LEAD (and more generally WP:MoS) contains lots of helpful advice (in case you haven't seen it). Geometry guy 11:11, 18 June 2007 (UTC)
[edit] First paragraph
Hi, I changed this: In probability theory, the definition of the probability space is the foundation of probability theory. to this: The definition of the probability space is the foundation of probability theory. which seems to make more sense.
It seems like there needs to be an informal (as accessible as possible and depending on as few specialized terms as necessary) definition of a Probability Space in that first paragraph though...
I don't know much about probability theory, and the fact that probability space is its foundation is an interesting fact, nevertheless it doesn't tell me what probability space is. —Preceding unsigned comment added by 157.193.108.159 (talk) 12:40, 26 October 2007 (UTC)
[edit] Usually?
It says "Usually, the events are the Lebesgue-measurable or Borel-measurable sets of real numbers." Shouldn't that be "If Omega is the set of real numbers (or R², R³ etc), then F is taken to be the Lebesgue-measurable or Borel-measurable sets". There are lots of applications of probability spaces which are based e.g. on a finite Omega.
Giese (talk) 09:45, 15 January 2008 (UTC)
