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On the covariance tensor

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Part of the Lecture Notes in Mathematics book series (LNM,volume 644)

Abstract

The concept of covariance, and the corollary concept of weak variance, are remarkably feebler in infinite-dimensional than in finite-dimensional spaces. This gives some indication of the weakness of such concepts as weak orthogonality in proving limit theorems for random variables in B-spaces.

Keywords

  • Banach Space
  • Bilinear Form
  • Conditional Independence
  • Weak Topology
  • Weak Variance

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Reference

  1. Anatole Beck, Conditional Independence, Zeitschrift für Wahrscheinlichkeitstheorie 33 (1976) pp. 253–267.

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© 1978 Springer-Verlag

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Beck, A. (1978). On the covariance tensor. In: Aron, R.M., Dineen, S. (eds) Vector Space Measures and Applications I. Lecture Notes in Mathematics, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066838

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  • DOI: https://doi.org/10.1007/BFb0066838

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08668-0

  • Online ISBN: 978-3-540-35906-7

  • eBook Packages: Springer Book Archive