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March 26th, 2013, 11:04 PM  #1  
Newbie Joined: Jan 2012 Posts: 12 Thanks: 0  Entropy H is continuous in p(i)
Here's something that I came across in "A Mathematical theory of communication" By Shannon that I couldn't get Quote:
What does he mean by H should be continuous in p(i) [where p(i) indicates probability of 'i' th event]. I couldn't get it.  
March 27th, 2013, 05:16 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 931 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Entropy H is continuous in p(i)
If p(i) changes by a very small amount, H will change by a small amount. You can use the normal epsilondelta definition here if you prefer.


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