Example of a metric over $D$ such that the $sigma$-algebras generated by the open sets and by the cylinders coincide

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$(D, mathcalB(D))$ where $D subset mathbbR^T$ is the set of cadlag functions over $T$.



Then, in my lecture notes, I have this statement:




There exists a metric over $D$ s.t. the $sigma$-Algebra generated by the open sets is equal to the $sigma$-Algebra generated by cylinders.




I would like to know any example of such metrics.




measure-theory




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    down vote

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    $(D, mathcalB(D))$ where $D subset mathbbR^T$ is the set of cadlag functions over $T$.



    Then, in my lecture notes, I have this statement:




    There exists a metric over $D$ s.t. the $sigma$-Algebra generated by the open sets is equal to the $sigma$-Algebra generated by cylinders.




    I would like to know any example of such metrics.




    measure-theory




    share|cite|improve this question























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      $(D, mathcalB(D))$ where $D subset mathbbR^T$ is the set of cadlag functions over $T$.



      Then, in my lecture notes, I have this statement:




      There exists a metric over $D$ s.t. the $sigma$-Algebra generated by the open sets is equal to the $sigma$-Algebra generated by cylinders.




      I would like to know any example of such metrics.




      measure-theory




      share|cite|improve this question













      $(D, mathcalB(D))$ where $D subset mathbbR^T$ is the set of cadlag functions over $T$.



      Then, in my lecture notes, I have this statement:




      There exists a metric over $D$ s.t. the $sigma$-Algebra generated by the open sets is equal to the $sigma$-Algebra generated by cylinders.




      I would like to know any example of such metrics.





      measure-theory





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Jul 30 at 13:48









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      asked Jul 30 at 13:22









      Melina

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