Blaschke selection theorem

<p>The Blaschke selection theorem is a result in <a href="/facts/Topology/2EqW47cU">topology</a> and <a href="/facts/Convex_geometry/tT3JL47B">convex geometry</a> about <a href="/facts/Sequence/gV2S4uqp">sequences</a> of <a href="/facts/Convex_set/vdAuJRJl">convex sets</a>.  Specifically, given a sequence 
  
    
      
        {
        
          K
          
            n
          
        
        }
      
    
    {\displaystyle \{K_{n}\}}
  
 of convex sets contained in a <a href="/facts/Bounded_set/yCldjtoy">bounded set</a>, the theorem guarantees the existence of a subsequence 
  
    
      
        {
        
          K
          
            
              n
              
                m
              
            
          
        
        }
      
    
    {\displaystyle \{K_{n_{m}}\}}
  
 and a convex set 
  
    
      
        K
      
    
    {\displaystyle K}
  
 such that 
  
    
      
        
          K
          
            
              n
              
                m
              
            
          
        
      
    
    {\displaystyle K_{n_{m}}}
  
 converges to 
  
    
      
        K
      
    
    {\displaystyle K}
  
 in the <a href="/facts/Hausdorff_metric/3tKbFmKu">Hausdorff metric</a>.  The theorem is named for <a href="/facts/Wilhelm_Blaschke/NQPEocq3">Wilhelm Blaschke</a>.
</p>

Blaschke selection theorem open-in-new

Blaschke selection theorem