Superadditive set function

<h2 id="definition">Definition</h2>
<p>Let 
  
    
      
        Ω
      
    
    {\displaystyle \Omega }
  
 be a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> and 
  
    
      
        f
        :
        
          2
          
            Ω
          
        
        →
        
          R
        
      
    
    {\displaystyle f\colon 2^{\Omega }\rightarrow \mathbb {R} }
  
 be a <a href="/facts/Set_function/Dy46B9EJ">set function</a>, where 
  
    
      
        
          2
          
            Ω
          
        
      
    
    {\displaystyle 2^{\Omega }}
  
 denotes the <a href="/facts/Power_set/FVuf8PDD">power set</a> of 
  
    
      
        Ω
      
    
    {\displaystyle \Omega }
  
. The function <i>f</i> is <i>superadditive</i> if for any pair of disjoint subsets 
  
    
      
        S
        ,
        T
      
    
    {\displaystyle S,T}
  
 of 
  
    
      
        Ω
      
    
    {\displaystyle \Omega }
  
, we have 
  
    
      
        f
        (
        S
        )
        +
        f
        (
        T
        )
        ≤
        f
        (
        S
        ∪
        T
        )
      
    
    {\displaystyle f(S)+f(T)\leq f(S\cup T)}
  
.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Utility_functions_on_indivisible_goods/fYTKPz7d">Utility functions on indivisible goods</a></li></ul>
<h2 id="citations">Citations</h2>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Nimrod Megiddo (1988). "ON FINDING ADDITIVE, SUPERADDITIVE AND SUBADDITIVE SET-FUNCTIONS SUBJECT TO LINEAR INEQUALITIES" (PDF). Retrieved 21 December 2015. <a href="http://theory.stanford.edu/~megiddo/pdf/Finding_supperadditiveX.pdf" target="_blank">http://theory.stanford.edu/~megiddo/pdf/Finding_supperadditiveX.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Superadditive set function open-in-new

Superadditive set function