Trivial sigma-algebra [on hold]

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My question is about the sigma-algebra acting as a filtration on probabilistic space.



What is the difference between the sigma-algebra and the trivial sigma-algebra ?




probability measure-theory probability-distributions actuarial-science filtrations




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put on hold as unclear what you're asking by Kavi Rama Murthy, m_t_, aduh, saz, amWhy yesterday


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 1




    I am not sure how a $sigma$-algebra acts as a filtration as in my understanding a filtration is a family of "increasing" $sigma$-algebras.
    – Jonas Lenz
    2 days ago











  • I think you are right. So, the trivial sigma-algebra will be the initial point of this "increasing" sigma-algebra ?
    – Hal03
    2 days ago






  • 1




    In my understanding yes, but it is not a single sigma-algebra but a family of sigma-algebras.
    – Jonas Lenz
    2 days ago










  • Thank you a lot!
    – Hal03
    2 days ago














up vote
0
down vote

favorite












My question is about the sigma-algebra acting as a filtration on probabilistic space.



What is the difference between the sigma-algebra and the trivial sigma-algebra ?




probability measure-theory probability-distributions actuarial-science filtrations




share|cite|improve this question











put on hold as unclear what you're asking by Kavi Rama Murthy, m_t_, aduh, saz, amWhy yesterday


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 1




    I am not sure how a $sigma$-algebra acts as a filtration as in my understanding a filtration is a family of "increasing" $sigma$-algebras.
    – Jonas Lenz
    2 days ago











  • I think you are right. So, the trivial sigma-algebra will be the initial point of this "increasing" sigma-algebra ?
    – Hal03
    2 days ago






  • 1




    In my understanding yes, but it is not a single sigma-algebra but a family of sigma-algebras.
    – Jonas Lenz
    2 days ago










  • Thank you a lot!
    – Hal03
    2 days ago












up vote
0
down vote

favorite









up vote
0
down vote

favorite











My question is about the sigma-algebra acting as a filtration on probabilistic space.



What is the difference between the sigma-algebra and the trivial sigma-algebra ?




probability measure-theory probability-distributions actuarial-science filtrations




share|cite|improve this question











My question is about the sigma-algebra acting as a filtration on probabilistic space.



What is the difference between the sigma-algebra and the trivial sigma-algebra ?





probability measure-theory probability-distributions actuarial-science filtrations





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked 2 days ago









Hal03

204




204




put on hold as unclear what you're asking by Kavi Rama Murthy, m_t_, aduh, saz, amWhy yesterday


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.






put on hold as unclear what you're asking by Kavi Rama Murthy, m_t_, aduh, saz, amWhy yesterday


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.









  • 1




    I am not sure how a $sigma$-algebra acts as a filtration as in my understanding a filtration is a family of "increasing" $sigma$-algebras.
    – Jonas Lenz
    2 days ago











  • I think you are right. So, the trivial sigma-algebra will be the initial point of this "increasing" sigma-algebra ?
    – Hal03
    2 days ago






  • 1




    In my understanding yes, but it is not a single sigma-algebra but a family of sigma-algebras.
    – Jonas Lenz
    2 days ago










  • Thank you a lot!
    – Hal03
    2 days ago












  • 1




    I am not sure how a $sigma$-algebra acts as a filtration as in my understanding a filtration is a family of "increasing" $sigma$-algebras.
    – Jonas Lenz
    2 days ago











  • I think you are right. So, the trivial sigma-algebra will be the initial point of this "increasing" sigma-algebra ?
    – Hal03
    2 days ago






  • 1




    In my understanding yes, but it is not a single sigma-algebra but a family of sigma-algebras.
    – Jonas Lenz
    2 days ago










  • Thank you a lot!
    – Hal03
    2 days ago







1




1




I am not sure how a $sigma$-algebra acts as a filtration as in my understanding a filtration is a family of "increasing" $sigma$-algebras.
– Jonas Lenz
2 days ago





I am not sure how a $sigma$-algebra acts as a filtration as in my understanding a filtration is a family of "increasing" $sigma$-algebras.
– Jonas Lenz
2 days ago













I think you are right. So, the trivial sigma-algebra will be the initial point of this "increasing" sigma-algebra ?
– Hal03
2 days ago




I think you are right. So, the trivial sigma-algebra will be the initial point of this "increasing" sigma-algebra ?
– Hal03
2 days ago




1




1




In my understanding yes, but it is not a single sigma-algebra but a family of sigma-algebras.
– Jonas Lenz
2 days ago




In my understanding yes, but it is not a single sigma-algebra but a family of sigma-algebras.
– Jonas Lenz
2 days ago












Thank you a lot!
– Hal03
2 days ago




Thank you a lot!
– Hal03
2 days ago















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