{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T00:40:16Z","timestamp":1694652016849},"reference-count":15,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2008,8,27]],"date-time":"2008-08-27T00:00:00Z","timestamp":1219795200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2008,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We define the effective integrability of Fine\u2010computable functions and effectivize some fundamental limit theorems in the theory of Lebesgue integrals such as the Bounded Convergence Theorem, the Dominated Convergence Theorem, and the Second Mean Value Theorem. It is also proved that the Walsh\u2010Fourier coefficients of an effectively integrable Fine\u2010computable function form a Euclidian computable sequence of reals which converges effectively to zero. This property of convergence is the effectivization of the Walsh\u2010Riemann\u2010Lebesgue Theorem. The article is closed with the effective version of Dirichlet's test. (\u00a9 2008 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710063","type":"journal-article","created":{"date-parts":[[2008,8,27]],"date-time":"2008-08-27T09:57:26Z","timestamp":1219831046000},"page":"519-534","source":"Crossref","is-referenced-by-count":1,"title":["Effective Fine\u2010convergence of Walsh\u2010Fourier series"],"prefix":"10.1002","volume":"54","author":[{"given":"Takakazu","family":"Mori","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mariko","family":"Yasugi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yoshiki","family":"Tsujii","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2008,8,27]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"382","article-title":"Some notes on Fine computability","volume":"8","author":"Brattka V.","year":"2002","journal-title":"J. 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