Abstract
We define and study new invariants called pre-image entropies which are similar to the standard notions of topological and measure-theoretic entropies. These new invariants are only non-zero for non-invertible maps, and they give a quantitative measurement of how far a given map is from being invertible. We obtain analogs of many known results for topological and measure-theoretic entropies. In particular, we obtain product rules, power rules, analogs of the Shannon–Breiman–McMillan theorem, and a variational principle.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
