I am reading Judea Pearl's "Causality" (second edition 2009) and in section 1.1.5 Conditional Independence and Graphoids, he states:


  The following is a (partial) list of properties satisfied by the 
  conditional independence relation (X_||_Y | Z). 
  
  
  Symmetry: (X_||_ Y | Z) ==> (Y_||_X | Z).
  Decomposition: (X_||_ YW | Z)  ==> (X_||_Y | Z).
  Weak union: (X_||_ YW | Z)  ==> (X_||_Y | ZW). 
  Contraction: (X_||_ Y | Z) &amp; (X_||_ W | ZY) ==> (X_||_ YW | Z).
  Intersection: (X_||_  W | ZY) &amp; (X_||_  Y | ZW) (X_||_  YW | Z). 
  
  
  (Intersection is valid in strictly positive probability distributions.)
  
  (formula (1.28) given earlier in the publicatiob: [(X_||_ Y | Z) iff P(X | Y,Z ) = P(X | Z)  )


But what is an  "strictly positive distribution" in general terms, and what distinguishes a "strictly positive distribution" form a distribution that is not strictly positive?


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