How to relate P(F) with P(F') where F' is F's closure (P(F)\neq 0)

[rukawakaede]

As title:

How do you relate P(F) with P(F') where F' is F's closure.

Conditions: P(F)\neq 0 and F non-empty.

My thought is P(F)=P(F').

Is this true?

 

[rukawakaede]

Now I understand that this depends on the probability measure and of course the set F itself. there is no general conclusion that could be draw for this situation.

 

[g_edgar]

In general, since F is a subset of its closure, the probability of F is less than or equal to the probability of the closure.

 

[rukawakaede]

In general, since F is a subset of its closure, the probability of F is less than or equal to the probability of the closure.

yes. thank you.