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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 8878
   School of Mathematics
  Title: Baire theorem in probabilistic modular spaces
  Author(s): K. Nourouzi
  Status: In Proceedings
  Proceeding: Proceedings of WCE 2008
  Year: 2008
  Supported by: IPM
  Abstract:
A real linear space X equipped with a probabilistic-valued function (! defined on X is called a probabilistic modular space if it satisfies the following conditions:

    i.ρx(0)=0,
    ii. ρx(t)=1 for all t > 0 iff x = 0,
    iii. ρx(t)=ρx(t),
    iv. ραxy(s+t) ≥ ρx(s)∧ρy(t) for all x,yX, and α, β, s, tR0+, α+ β = 1
In this note, we give a modular formulation of Baire's Theorem in probabilistic modular spaces.


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