{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T16:01:36Z","timestamp":1743004896547,"version":"3.40.3"},"publisher-location":"Cham","reference-count":15,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319200279"},{"type":"electronic","value":"9783319200286"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-20028-6_20","type":"book-chapter","created":{"date-parts":[[2015,6,19]],"date-time":"2015-06-19T10:07:37Z","timestamp":1434708457000},"page":"196-205","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Randomness and Differentiability of Convex Functions"],"prefix":"10.1007","author":[{"given":"Alex","family":"Galicki","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,6,20]]},"reference":[{"key":"20_CR1","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/PL00004691","volume":"230","author":"G Alberti","year":"1999","unstructured":"Alberti, G., Ambrosio, L.: A geometrical approach to monotone functions in $$\\mathbb{R}^n$$. Math. Z. 230, 259\u2013316 (1999)","journal-title":"Math. Z."},{"key":"20_CR2","first-page":"3","volume":"6","author":"AD Aleksandrov","year":"1939","unstructured":"Aleksandrov, A.D.: Leningrad Univ. Ann. (Math. Ser.) 6, 3\u201335 (1939)","journal-title":"Leningrad Univ. Ann. (Math. Ser.)"},{"key":"20_CR3","unstructured":"Brattka, V., Miller, J., Nies, A.: Randomness and differentiability. Trans. AMS (forthcoming). http:\/\/arxiv.org\/abs\/1104.4465"},{"issue":"1","key":"20_CR4","first-page":"70","volume":"2","author":"D Dingzhu","year":"1989","unstructured":"Dingzhu, D., Ko, K.: Computational complexity of integration and differentiation of convex functions. Syst. Sci. Math. Sci. 2(1), 70\u201379 (1989)","journal-title":"Syst. Sci. Math. Sci."},{"key":"20_CR5","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.: Algorithmic Randomness and Complexity. Springer, Berlin (2010)"},{"issue":"1","key":"20_CR6","doi-asserted-by":"crossref","first-page":"45","DOI":"10.3233\/COM-14025","volume":"3","author":"C Freer","year":"2014","unstructured":"Freer, C., Kjos-Hanssen, B., Nies, A., Stephan, F.: Algorithmic aspects of lipschitz functions. Computability 3(1), 45\u201361 (2014)","journal-title":"Computability"},{"key":"20_CR7","unstructured":"Galicki, A., Turetsky, D.: Differentiability and randomness in higher dimensions (2014, Submitted)"},{"key":"20_CR8","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1215\/S0012-7094-62-02933-2","volume":"29","author":"G Minty","year":"1962","unstructured":"Minty, G.: Monotone nonlinear operators on a Hilbert space. Duke Math J. 29, 341\u2013346 (1962)","journal-title":"Duke Math J."},{"key":"20_CR9","series-title":"Oxford Logic Guides","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199230761.001.0001","volume-title":"Computability and Randomness","author":"A Nies","year":"2009","unstructured":"Nies, A.: Computability and Randomness. Oxford Logic Guides. Oxford University Press, Oxford (2009)"},{"key":"20_CR10","volume-title":"Computability in Analysis and Physics","author":"MB Pour-El","year":"1988","unstructured":"Pour-El, M.B., Richards, I.: Computability in Analysis and Physics. Springer, Berlin (1988)"},{"key":"20_CR11","series-title":"Grundlehren der Mathematischen Wissenschaften","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"1997","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Grundlehren der Mathematischen Wissenschaften. Springer, Heidelberg (1997)"},{"key":"20_CR12","unstructured":"Rute. J.: Computable randomness and betting for computable probability spaces (2012, Submitted)"},{"key":"20_CR13","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1016\/S0096-3003(02)00932-3","volume":"148","author":"S Siksek","year":"2004","unstructured":"Siksek, S., El Sedy, E.: Points of non-differentiability of convex functions. Appl. Math. Comput. 148, 725\u2013728 (2004)","journal-title":"Appl. Math. Comput."},{"key":"20_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56999-9","volume-title":"Computable Analysis","author":"K Weihrauch","year":"2000","unstructured":"Weihrauch, K.: Computable Analysis. Springer, Berlin (2000)"},{"key":"20_CR15","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1002\/malq.19980440303","volume":"44","author":"N Zhong","year":"1998","unstructured":"Zhong, N.: Derivatives of computable functions. Math. Log. Q. 44, 304\u2013316 (1998)","journal-title":"Math. Log. Q."}],"container-title":["Lecture Notes in Computer Science","Evolving Computability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-20028-6_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,24]],"date-time":"2023-01-24T13:23:27Z","timestamp":1674566607000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-20028-6_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319200279","9783319200286"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-20028-6_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"20 June 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}