- #1

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Hi all,

is sample space an open set or a closed set?

Thanks in advance

is sample space an open set or a closed set?

Thanks in advance

- Thread starter woundedtiger4
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- #1

- 189

- 0

Hi all,

is sample space an open set or a closed set?

Thanks in advance

is sample space an open set or a closed set?

Thanks in advance

- #2

chiro

Science Advisor

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What do you mean by sample space exactly?

If you have a set with a finite number of elements, it has to be closed by default but if you are talking about some arbitrary region, then it may be different.

The reason I say the above is that if you are talking about a sample in statistics, a sample is always finite that is drawn from either an infinite population or a finite one (like for example when you have populations like the people in an entire country or state which is used in survey design as an example).

- #3

chiro

Science Advisor

- 4,790

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What do you mean by sample space exactly?

If you have a set with a finite number of elements, it has to be closed by default but if you are talking about some arbitrary region, then it may be different.

The reason I say the above is that if you are talking about a sample in statistics, a sample is always finite that is drawn from either an infinite population or a finite one (like for example when you have populations like the people in an entire country or state which is used in survey design as an example).

- #4

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Whatever you like. Any set will do, as far as I know.Hi all,

is sample space an open set or a closed set?

Thanks in advance

- #5

chiro

Science Advisor

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Is the sample a statistical sample or something else?

- #6

mathman

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A sample space is not required to have a topology, so open or closed is besides the point.

- #7

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why?A sample space is not required to have a topology, so open or closed is besides the point.

Edited: I mean why it doesn't require topology?

Last edited:

- #8

Stephen Tashi

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Whether you must have a toplogy to do probability theory is an interesting question. To view probability from the point of view of masure theory, you must have a "sigma algebra" of sets. Some of the axioms for a sigma algebra are very similar to those for a toplogy, but according to this discussion http://mathoverflow.net/questions/70137/sigma-algebra-that-is-not-a-topology , a sigma algebra need not be a toplogy. From that point of view, you can do probability theory without a topology.

If you are taking a course that focuses on applications of probability and doing summations or integrations of functions defined on real numbers then your course assumes the "usual" topology for 1 or n-dimensional euclidean space.

- #9

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Your sample space can be a housecat, an anchovy pizza, and a Mohair-covered Caddillac. So no, you don't need a topology.

Whether you must have a toplogy to do probability theory is an interesting question. To view probability from the point of view of masure theory, you must have a "sigma algebra" of sets. Some of the axioms for a sigma algebra are very similar to those for a toplogy, but according to this discussion http://mathoverflow.net/questions/70137/sigma-algebra-that-is-not-a-topology , a sigma algebra need not be a toplogy. From that point of view, you can do probability theory without a topology.

If you are taking a course that focuses on applications of probability and doing summations or integrations of functions defined on real numbers then your course assumes the "usual" topology for 1 or n-dimensional euclidean space.

- #10

- 189

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excellent explanation......... thanks

Whether you must have a toplogy to do probability theory is an interesting question. To view probability from the point of view of masure theory, you must have a "sigma algebra" of sets. Some of the axioms for a sigma algebra are very similar to those for a toplogy, but according to this discussion http://mathoverflow.net/questions/70137/sigma-algebra-that-is-not-a-topology , a sigma algebra need not be a toplogy. From that point of view, you can do probability theory without a topology.

If you are taking a course that focuses on applications of probability and doing summations or integrations of functions defined on real numbers then your course assumes the "usual" topology for 1 or n-dimensional euclidean space.

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