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The Nucleus of a Set

Published online by Cambridge University Press:  20 November 2018

Gilbert Strang
Gilbert Strang*
Affiliation:
Massachusetts Institute of Technology
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Consider the subset containing those functions for which

One never attempts to visualize ; it is just a compact blur in the infinite-dimensional space . Nevertheless, we want to establish that it shares with several other sets an odd but rather remarkable "geometric" property: it is overwhelmingly concentrated around a single element. This element we call the nucleus of .

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 1 , April 1968 , pp. 65 - 72
Copyright
Copyright © Canadian Mathematical Society 1968

References

1 Kolmogorov, A.N. and Tihomirov, V.M., ∈-entropy and ∈ - capacity of sets in functional spaces, Uspehi Mat. 14(1959) 3-86; American Math, Soc. Translations 17 (1961) 277–364.Google Scholar