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My book defined 'outcome space', but then went ahead and used the term 'sample space' without definition.

The collection of all possible outcomes [of a random experiment] is called the outcome space.

In an example, my book said the following:

A fair six-sided die is rolled six times. If the face numbered $k$ is the outcome on roll $k$ for $k=1, 2, ..., 6$, we say that a match has occurred. The experient is called a success if at least one match occurs during the six trials. Otherwise, the experiment is called a failure. The sample space is {success, failure}. Let A = {success}...

Are these two words synonymous? If not, what are their meanings? Also, is there some reason why the sample/outcome space is called a space as opposed to a set?

EDIT:

The book is Probability and Statistical Inference by Hogg, Tanis, Zimmerman, 9th edition, Global edition. ISBN-10:1-292-06235-5

The first quote is from page 10. The second is on page 13.

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  • $\begingroup$ Can you link to the book you are referring to? $\endgroup$
    – Antoni Parellada
    Commented May 15, 2017 at 23:35
  • $\begingroup$ @AntoniParellada I edited the question with that information. $\endgroup$
    – Ovi
    Commented May 16, 2017 at 0:02
  • $\begingroup$ I found this thread on the topic. $\endgroup$
    – Antoni Parellada
    Commented May 16, 2017 at 0:39
  • $\begingroup$ Regarding the thread on physicsforums.com mentioned in the comment above by @AntoniParellada: I disagree with response #2 there by StatsTiger. A brief summary of StatsTiger's interpretation is e.g., for rolling a pair of dice, the outcome space is $\{(1,1), (1,2), \ldots, (6,6)\}$ where as the sample space is still $\{1, 2, \ldots, 6\}$ - this is incorrect. The other responses on that thread are fine. $\endgroup$
    – Just_to_Answer
    Commented May 16, 2017 at 3:21

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They are synonymous - both define the possible samples you can get from your experiment. Why are they called spaces? In mathematics, a "space" is not just a set, but implies there is some relationship among the members of the set.

For example $\{A,B,C\}$ is just a set of three objects, but if they represent an alphabet, we can call it a 'lexical space' or something like that.

Here's an interesting paper discussing spaces vs sets.

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