Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Joint measures and cross-covariance operators
HTML articles powered by AMS MathViewer

by Charles R. Baker PDF
Trans. Amer. Math. Soc. 186 (1973), 273-289 Request permission

Abstract:

Let ${H_1}$ (resp., ${H_2}$) be a real and separable Hilbert space with Borel $\sigma$-field ${\Gamma _1}$ (resp., ${\Gamma _2}$), and let $({H_1} \times {H_2},{\Gamma _1} \times {\Gamma _2})$ be the product measurable space generated by the measurable rectangles. This paper develops relations between probability measures on $({H_1} \times {H_2},{\Gamma _1} \times {\Gamma _2})$, i.e., joint measures, and the projections of such measures on $({H_1},{\Gamma _1})$ and $({H_2},{\Gamma _2})$. In particular, the class of all joint Gaussian measures having two specified Gaussian measures as projections is characterized, and conditions are obtained for two joint Gaussian measures to be mutually absolutely continuous. The cross-covariance operator of a joint measure plays a major role in these results and these operators are characterized.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 60G15, 28A40
  • Retrieve articles in all journals with MSC: 60G15, 28A40
Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 186 (1973), 273-289
  • MSC: Primary 60G15; Secondary 28A40
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0336795-3
  • MathSciNet review: 0336795