Regular variation for non-negative functions

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I only found regular variation defined for positive functions. Can it also be defined for functions that take value $0$, especially if it's just at one point ($f(0) = 0$) and the function is non-decreasing?




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    I only found regular variation defined for positive functions. Can it also be defined for functions that take value $0$, especially if it's just at one point ($f(0) = 0$) and the function is non-decreasing?




    real-analysis probability-theory functions




    share|cite|improve this question























      up vote
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      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I only found regular variation defined for positive functions. Can it also be defined for functions that take value $0$, especially if it's just at one point ($f(0) = 0$) and the function is non-decreasing?




      real-analysis probability-theory functions




      share|cite|improve this question













      I only found regular variation defined for positive functions. Can it also be defined for functions that take value $0$, especially if it's just at one point ($f(0) = 0$) and the function is non-decreasing?





      real-analysis probability-theory functions





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Jul 17 at 23:24









      RayDansh

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      asked Jul 17 at 23:21









      Janusz Lezak

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