Theoretical analysis demonstrates the existence of maximum entropy probability distributions under convex constraints, highlighting topological solutions for complex continuous variables.
In this paper, we consider a Differential Entropy Maximization Problem when standard techniques are not suitable. We use a purely topological Fan-KKM Theorem to prove the existence of a maximum entropy probability distribution with general closed and convex constraints for an Effective Counting Entropy functional of a special class of continuous random variables with values in [0,a] such that the probability density functions are nonnegative and have finite second moments.
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Li et al. (2026) studied this question.
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