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

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Discussion Overview

The discussion centers on the relationship between the probability of a set F and the probability of its closure F', under the condition that P(F) is not equal to zero and F is non-empty. Participants explore whether P(F) can be equated to P(F') and the implications of the probability measure involved.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes that P(F) could equal P(F').
  • Another participant notes that the relationship depends on the specific probability measure and the characteristics of the set F, indicating that no general conclusion can be drawn.
  • It is mentioned that since F is a subset of its closure, the probability of F is less than or equal to the probability of the closure.
  • A later reply agrees with the point about the subset relationship and the associated probabilities.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between P(F) and P(F'). While one participant suggests equality, others highlight the dependence on the probability measure and the nature of F, indicating that the discussion remains unresolved.

Contextual Notes

The discussion does not resolve the assumptions regarding the probability measure or the specific properties of the set F that might affect the relationship between P(F) and P(F').

rukawakaede
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As title:

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

Conditions: [tex]P(F)\neq 0[/tex] and F non-empty.

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

Is this true?
 
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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.
 
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.
 
g_edgar said:
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.
 

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