| 
 
            
               
            
            his section lists some common notations. 
            
               
            
              is an open subset of  .  is the boundary of  .  is the closure of  . 
            
               
            
              . 
            
               
            
               
            
               
            
              . 
            
               
            
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              . 
            
               
            
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               For a function
               
            
              we
               denote 
               where the
                |   |  | (ess sup definition) |   is the Lebesgue measure (see the proposition
               (
            
              Existence of Lebesgue
                measure
            
            )). 
            
               
            
              , 
            
               
            
               
            
               
            
               
            
               
            
              . 
            
               
            
              ,   
            
               
            
              is the "Schwartz space" of infinitely differentiable functions  such
               that for any polynomial  of finite dimension and any multi-index  we
               have 
               
                |   |  | (Schwartz space) |  |