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mw19930312
mw19930312
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I'm exploring the possibility to apply information theory on an uncountably infinite-dimensional scenario. I found the concept of `generalized entropy'generalized entropy for continuous random variables defined on finite-dimensional Euclidean space. I wonder whether there are similar concepts for uncountably infinite-dimensional cases. For instance, if I have a distribution on $C([0, 1])$, which is the space of continuous function on $[0, 1]$, then how can I quantify the entropy of this distribution?

I'm exploring the possibility to apply information theory on an uncountably infinite-dimensional scenario. I found the concept of `generalized entropy' for continuous random variables defined on finite-dimensional Euclidean space. I wonder whether there are similar concepts for uncountably infinite-dimensional cases. For instance, if I have a distribution on $C([0, 1])$, which is the space of continuous function on $[0, 1]$, then how can I quantify the entropy of this distribution?

I'm exploring the possibility to apply information theory on an uncountably infinite-dimensional scenario. I found the concept of generalized entropy for continuous random variables defined on finite-dimensional Euclidean space. I wonder whether there are similar concepts for uncountably infinite-dimensional cases. For instance, if I have a distribution on $C([0, 1])$, which is the space of continuous function on $[0, 1]$, then how can I quantify the entropy of this distribution?

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mw19930312
mw19930312
  • 263
  • 1
  • 6

Information theory for uncountably infinite-dimensional continuous random variable

I'm exploring the possibility to apply information theory on an uncountably infinite-dimensional scenario. I found the concept of `generalized entropy' for continuous random variables defined on finite-dimensional Euclidean space. I wonder whether there are similar concepts for uncountably infinite-dimensional cases. For instance, if I have a distribution on $C([0, 1])$, which is the space of continuous function on $[0, 1]$, then how can I quantify the entropy of this distribution?