A Uniform Ergodic Theorem
نویسندگان
چکیده
منابع مشابه
Uniform Integrability and the Pointwtse Ergodic Theorem
Let iX, 03, m) be a finite measure space. We shall denote by L*im) (1 èp< °°) the Banach space of all real-valued (B-measurable functions/ defined on X such that |/[ p is m-integrable, and by L°°(w) the Banach space of all real-valued, (B-measurable, w-essentially bounded functions defined on X; as usual, the norm in Lpim) is given by 11/11,.= {fx\fix)\pdm}1'*, and the norm in Lxim) by \\g\\x =...
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متن کاملErgodic theorem, ergodic theory, and statistical mechanics.
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1965
ISSN: 0003-4851
DOI: 10.1214/aoms/1177699815