منابع مشابه
Kingman's Subadditive Ergodic Theorem Kingman's Subadditive Ergodic Theorem
A simple proof of Kingman’s subadditive ergodic theorem is developed from a point of view which is conceptually algorithmic and which does not rely on either a maximal inequality or a combinatorial Riesz lemma.
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To justify the use of sampling to solve stochastic programming problems one usually relies on a law of large numbers for random lsc (lower semicontinuous) functions when the samples come from independent, identical experiments. If the samples come from a stationary process, one can appeal to the ergodic theorem proved here. The proof relies on thèscalarization' of random lsc functions.
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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: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1968
ISSN: 0386-2194
DOI: 10.3792/pja/1195521330