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Published May 2017 | Submitted
Journal Article Open

Separability of reproducing kernel Hilbert spaces


We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.

Additional Information

© 2016 American Mathematical Society. Received by the editors July 13, 2015 and, in revised form, March 3, 2016, May 31, 2016, and July 5, 2016. The authors would like to thank the referees for comments and suggestions which substantially improved both the content and the presentation of this work. The authors gratefully acknowledge the support of the Air Force Office of Scientific Research under award number FA9550-12-1-0389 (Scientific Computation of Optimal Statistical Estimators) and AFOSR/DARPA EQUiPS grant number FA9550-16-1- 0054 (Computational Information Games).

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