LEADER 03138nam 2200517 450 001 9910672435203321 005 20240129123815.0 010 $a9783031231223$b(electronic bk.) 010 $z9783031231216 024 7 $a10.1007/978-3-031-23122-3 035 $a(MiAaPQ)EBC7207345 035 $a(Au-PeEL)EBL7207345 035 $a(CKB)26186117500041 035 $a(DE-He213)978-3-031-23122-3 035 $a(PPN)268204985 035 $a(EXLCZ)9926186117500041 100 $a20230522d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGaussian Measures in Finite and Infinite Dimensions /$fDaniel W. Stroock 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer Nature Switzerland AG,$d[2023] 210 4$d©2023 215 $a1 online resource (152 pages) 225 1 $aUniversitext Series 311 08$aPrint version: Stroock, Daniel W. Gaussian Measures in Finite and Infinite Dimensions Cham : Springer International Publishing AG,c2023 9783031231216 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1. Characteristic Functions -- 2. Gaussian Measures and Families -- 3. Gaussian Measures on a Banach Space -- 4. Further Properties and Examples of Abstract Wiener Spaces -- References -- Index. 330 $aThis text provides a concise introduction, suitable for a one-semester special topics course, to the remarkable properties of Gaussian measures on both finite and infinite dimensional spaces. It begins with a brief resumé of probabilistic results in which Fourier analysis plays an essential role, and those results are then applied to derive a few basic facts about Gaussian measures on finite dimensional spaces. In anticipation of the analysis of Gaussian measures on infinite dimensional spaces, particular attention is given to those properties of Gaussian measures that are dimension independent, and Gaussian processes are constructed. The rest of the book is devoted to the study of Gaussian measures on Banach spaces. The perspective adopted is the one introduced by I. Segal and developed by L. Gross in which the Hilbert structure underlying the measure is emphasized. The contents of this book should be accessible to either undergraduate or graduate students who are interested in probability theory and have a solid background in Lebesgue integration theory and a familiarity with basic functional analysis. Although the focus is on Gaussian measures, the book introduces its readers to techniques and ideas that have applications in other contexts. 410 0$aUniversitext. 606 $aGaussian measures 606 $aMesures gaussianes$2thub 608 $aLlibres electrònics$2thub 615 0$aGaussian measures. 615 7$aMesures gaussianes 676 $a515.42 700 $aStroock$b Daniel W.$042628 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910672435203321 996 $aGaussian Measures in Finite and Infinite Dimensions$93051223 997 $aUNINA