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.
Best Answer
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.