Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

``Lebesgue measure'' on $ {\bf R}\sp \infty$


Author: Richard Baker
Journal: Proc. Amer. Math. Soc. 113 (1991), 1023-1029
MSC: Primary 46G12; Secondary 28A35, 28C20
MathSciNet review: 1062827
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We construct a translation invariant Borel measure $ \lambda $ on $ {{\mathbf{R}}^\infty } = \prod _{i = 1}^\infty {\mathbf{R}}$ such that for any infinite-dimensional rectangle $ R = \prod _{i = 1}^\infty ({a_i},{b_i}), - \infty < {a_i} \leq {b_i} < + \infty $, if $ 0 \leq \prod _{i = 1}^\infty ({b_i} - {a_i}) < + \infty $, then $ \lambda (R) = \prod _{i = 1}^\infty ({b_i} - {a_i})$. Because $ {{\mathbf{R}}^\infty }$ is an infinite-dimensional locally convex topological vector space, the measure $ \lambda $ can not be $ \sigma $-finite.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46G12, 28A35, 28C20

Retrieve articles in all journals with MSC: 46G12, 28A35, 28C20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062827-X
PII: S 0002-9939(1991)1062827-X
Article copyright: © Copyright 1991 American Mathematical Society