"Non UBC"@en . "DSpace"@en . "Duenez, Eduardo"@en . "2019-03-24T05:04:25Z"@en . "2018-06-12T12:09"@en . "We revisit certain classical and recent results on convergence of\naverages of a fixed element f of a topological vector space V endowed\nwith an action (g,f)\u00E2 \u00A6 \u00E1\u00B5 f of an amenable (semi)group G. (In the special\ncase when G = \u00E2 is the semigroup of naturals, the averages are just (\u00C2\u00B9f\n+ \u00C2\u00B2f + \u00E2 \u00AF + \u00E2 \u00BFf)/n). Such results, collectively called ergodic convergence\ntheorems\u00E2 although there is really nothing \u00E2 ergodic\u00E2 about them\u00E2 ,\ninclude the classical ergodic theorem of Birkhoff as well as von\nNeumann\u00E2 s mean ergodic theorem (MET), alongside subsequent\ngeneralizations. In collaboration with J. Iovino, we use continuous\nlogic to obtain a radically elementary proof of a MET valid for any\npolynomial action of an amenable group on a Hilbert space. The\nCompactness Theorem from logic implies the existence of universal\nrates of metastable convergence that depend only on the degree of the\naction."@en . "https://circle.library.ubc.ca/rest/handle/2429/69167?expand=metadata"@en . "42.0"@en . "video/mp4"@en . ""@en . "Author affiliation: Spelman College"@en . "10.14288/1.0377409"@en . "eng"@en . "Unreviewed"@en . "Vancouver : University of British Columbia Library"@en . "Banff International Research Station for Mathematical Innovation and Discovery"@en . "Attribution-NonCommercial-NoDerivatives 4.0 International"@en . "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en . "Researcher"@en . "BIRS Workshop Lecture Videos (Oaxaca de Ju\u00E1rez (Mexico))"@en . "Mathematics"@en . "Math science education"@en . "Metastable convergence of ergodic averages: The continuous logic viewpoint."@en . "Moving Image"@en . "http://hdl.handle.net/2429/69167"@en .