{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T23:53:58Z","timestamp":1725753238510},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642449574"},{"type":"electronic","value":"9783642449581"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-44958-1_21","type":"book-chapter","created":{"date-parts":[[2013,10,22]],"date-time":"2013-10-22T10:54:01Z","timestamp":1382439241000},"page":"273-284","source":"Crossref","is-referenced-by-count":0,"title":["An Optimal Superfarthingale and Its Convergence over a Computable Topological Space"],"prefix":"10.1007","author":[{"given":"Kenshi","family":"Miyabe","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"21_CR1","doi-asserted-by":"publisher","first-page":"278","DOI":"10.2307\/2981683","volume":"147","author":"A.P. Dawid","year":"1984","unstructured":"Dawid, A.P.: Statistical theory: the prequential approach (with discussion). Journal of the Royal Statistical Society A\u00a0147, 278\u2013292 (1984)","journal-title":"Journal of the Royal Statistical Society A"},{"key":"21_CR2","doi-asserted-by":"publisher","first-page":"125","DOI":"10.2307\/3318616","volume":"5","author":"A.P. Dawid","year":"1999","unstructured":"Dawid, A.P., Vovk, V.: Prequential probability: principles and properties. Bernoulli\u00a05, 125\u2013162 (1999)","journal-title":"Bernoulli"},{"key":"21_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68441-3","volume-title":"Algorithmic Randomness and Complexity","author":"R. Downey","year":"2010","unstructured":"Downey, R., Hirschfeldt, D.R.: Algorithmic Randomness and Complexity. Springer, Berlin (2010)"},{"key":"21_CR4","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1090\/S0002-9939-2010-10513-0","volume":"139","author":"J.N.Y. Franklin","year":"2011","unstructured":"Franklin, J.N.Y., Ng, K.M.: Difference randomness. Proc. Amer. Math. Soc.\u00a0139, 345\u2013360 (2011)","journal-title":"Proc. Amer. Math. Soc."},{"key":"21_CR5","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.tcs.2005.03.054","volume":"341","author":"P. G\u00e1cs","year":"2005","unstructured":"G\u00e1cs, P.: Uniform test of algorithmic randomness over a general space. Theoretical Computer Science\u00a0341, 91\u2013137 (2005)","journal-title":"Theoretical Computer Science"},{"issue":"4-5","key":"21_CR6","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1002\/malq.200710009","volume":"53","author":"T. Grubba","year":"2007","unstructured":"Grubba, T., Schr\u00f6der, M., Weihrauch, K.: Computable metrization. Mathematical Logic Quaterly\u00a053(4-5), 381\u2013395 (2007)","journal-title":"Mathematical Logic Quaterly"},{"key":"21_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1007\/978-3-642-03073-4_27","volume-title":"Mathematical Theory and Computational Practice","author":"M. Hoyrup","year":"2009","unstructured":"Hoyrup, M., Rojas, C.: An Application of Martin-L\u00f6f Randomness to Effective Probability Theory. In: Ambos-Spies, K., L\u00f6we, B., Merkle, W. (eds.) CiE 2009. LNCS, vol.\u00a05635, pp. 260\u2013269. Springer, Heidelberg (2009)"},{"issue":"7","key":"21_CR8","doi-asserted-by":"publisher","first-page":"830","DOI":"10.1016\/j.ic.2008.12.009","volume":"207","author":"M. Hoyrup","year":"2009","unstructured":"Hoyrup, M., Rojas, C.: Computability of probability measures and Martin-L\u00f6f randomness over metric spaces. Information and Computation\u00a0207(7), 830\u2013847 (2009)","journal-title":"Information and Computation"},{"key":"21_CR9","unstructured":"Hutter, M.: Universal artificial intelligence: Sequential decisions based on algorithmic probability. Springer (2005)"},{"key":"21_CR10","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.tcs.2007.03.040","volume":"382","author":"M. Hutter","year":"2007","unstructured":"Hutter, M., Muchnik, A.: On semimeasures predicting Martin-L\u00f6f random sequences. Theoretical Computer Science\u00a0382, 247\u2013261 (2007)","journal-title":"Theoretical Computer Science"},{"key":"21_CR11","series-title":"Graduate Texts in Computer Science","volume-title":"An introduction to Kolmogorov complexity and its applications","author":"M. Li","year":"2009","unstructured":"Li, M., Vit\u00e1nyi, P.: An introduction to Kolmogorov complexity and its applications, 3rd edn. Graduate Texts in Computer Science. Springer, New York (2009)","edition":"3"},{"key":"21_CR12","unstructured":"Miyabe, K.: Algorithmic randomness over general spaces (submitted)"},{"key":"21_CR13","doi-asserted-by":"crossref","unstructured":"Nies, A.: Computability and Randomness. Oxford University Press, USA (2009)","DOI":"10.1093\/acprof:oso\/9780199230761.001.0001"},{"key":"21_CR14","unstructured":"Odifreddi, P.: Classical Recursion Theory, vol.\u00a01. North-Holland (1990)"},{"key":"21_CR15","unstructured":"Odifreddi, P.: Classical Recursion Theory, vol.\u00a02. North-Holland (1999)"},{"issue":"4-5","key":"21_CR16","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1002\/malq.200710010","volume":"53","author":"M. Schr\u00f6der","year":"2007","unstructured":"Schr\u00f6der, M.: Admissible Representations for Probability Measures. Mathematical Logic Quarterly\u00a053(4-5), 431\u2013445 (2007)","journal-title":"Mathematical Logic Quarterly"},{"key":"21_CR17","doi-asserted-by":"crossref","unstructured":"Shafer, G., Vovk, V.: Probability and Finance: It\u2019s Only a Game! Wiley (2001)","DOI":"10.1002\/0471249696"},{"key":"21_CR18","series-title":"Perspectives in Mathematical Logic","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02460-7","volume-title":"Recursively enumerable sets and degrees","author":"R.I. Soare","year":"1987","unstructured":"Soare, R.I.: Recursively enumerable sets and degrees. Perspectives in Mathematical Logic. Springer, Berlin (1987)"},{"key":"21_CR19","doi-asserted-by":"crossref","unstructured":"Solomonoff, R.J.: A formal theory of inductive inference I, II. Information and Control\u00a07, 1\u201322, 224\u2013254 (1964)","DOI":"10.1016\/S0019-9958(64)90131-7"},{"key":"21_CR20","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1109\/TIT.1978.1055913","volume":"24","author":"R.J. Solomonoff","year":"1978","unstructured":"Solomonoff, R.J.: Complexity-based induction systems: Comparisons and convergence theorems. IEEE Transaction on Information Theory IT\u00a024, 422\u2013432 (1978)","journal-title":"IEEE Transaction on Information Theory IT"},{"key":"21_CR21","doi-asserted-by":"publisher","first-page":"2632","DOI":"10.1016\/j.tcs.2010.04.002","volume":"411","author":"V. Vovk","year":"2010","unstructured":"Vovk, V., Shen, A.: Prequential randomness and probability. Theoretical Computer Science\u00a0411, 2632\u20132646 (2010)","journal-title":"Theoretical Computer Science"},{"key":"21_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56999-9","volume-title":"Computable Analysis: an introduction","author":"K. Weihrauch","year":"2000","unstructured":"Weihrauch, K.: Computable Analysis: an introduction. Springer, Berlin (2000)"},{"issue":"6","key":"21_CR23","first-page":"1381","volume":"15","author":"K. Weihrauch","year":"2009","unstructured":"Weihrauch, K., Grubba, T.: Elementary Computable Topology. Journal of Universal Computer Science\u00a015(6), 1381\u20131422 (2009)","journal-title":"Journal of Universal Computer Science"},{"key":"21_CR24","unstructured":"Weihrauch, K.: Computable Separation in Topology, from T\n                           0 to T\n                           3. In: CCA (2009)"}],"container-title":["Lecture Notes in Computer Science","Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-44958-1_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T18:40:20Z","timestamp":1558636820000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-44958-1_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642449574","9783642449581"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-44958-1_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}