Abstract
So far we have looked at systems described by piecewise bijective functions.
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Notes
- 1.
There are examples for one-dimensional RVs with finite differential entropy that satisfy \(H(\hat{X}^{(0)})=\infty \), hence \(d(X)=\infty \) [Ré59, Remark after Theorem 1].
- 2.
The authors thank Delcho Donev for motivating this result.
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Geiger, B.C., Kubin, G. (2018). Dimensionality-Reducing Functions. In: Information Loss in Deterministic Signal Processing Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-59533-7_4
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DOI: https://doi.org/10.1007/978-3-319-59533-7_4
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