LEADER 03734nam 22006255 450 001 9910986138703321 005 20251103115057.0 010 $a9789819779291 010 $a9819779294 024 7 $a10.1007/978-981-97-7929-1 035 $a(CKB)37817223500041 035 $a(MiAaPQ)EBC31955430 035 $a(Au-PeEL)EBL31955430 035 $a(OCoLC)1506226818 035 $a(DE-He213)978-981-97-7929-1 035 $a(EXLCZ)9937817223500041 100 $a20250310d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMeasure Theory for Analysis and Probability /$fby Alok Goswami, B.V. Rao 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (387 pages) 225 1 $aIndian Statistical Institute Series,$x2523-3122 311 08$a9789819779284 311 08$a9819779286 327 $a1. Measure Theory: Why and What -- 2. Measures: Construction and Properties -- 3. Measurable Functions and Integration -- 4. Random Variables and Random Vectors -- 5. Product Spaces -- 6. Radon-Nikodym Theorem and Lp Spaces -- 7. Convergence and Laws of Large Numbers -- 8. Weak convergence and Central Limit Theorem -- 9. Conditioning: The Right Approach -- 10. Infinite Products -- 11. Brownian Motion: A Brief Journey. 330 $aThis book covers major measure theory topics with a fairly extensive study of their applications to probability and analysis. It begins by demonstrating the essential nature of measure theory before delving into the construction of measures and the development of integration theory. Special attention is given to probability spaces and random variables/vectors. The text then explores product spaces, Radon?Nikodym and Jordan?Hahn theorems, providing a detailed account of ???????? spaces and their duals. After revisiting probability theory, it discusses standard limit theorems such as the laws of large numbers and the central limit theorem, with detailed treatment of weak convergence and the role of characteristic functions. The book further explores conditional probabilities and expectations, preceded by motivating discussions. It discusses the construction of probability measures on infinite product spaces, presenting Tulcea?s theorem and Kolmogorov?s consistency theorem. The text concludes with the construction of Brownian motion, examining its path properties and the significant strong Markov property. This comprehensive guide is invaluable not only for those pursuing probability theory seriously but also for those seeking a robust foundation in measure theory to advance in modern analysis. By effectively motivating readers, it underscores the critical role of measure theory in grasping fundamental probability concepts. 410 0$aIndian Statistical Institute Series,$x2523-3122 606 $aMeasure theory 606 $aProbabilities 606 $aMeasure and Integration 606 $aProbability Theory 606 $aTeoria de la mesura$2thub 606 $aProbabilitats$2thub 608 $aLlibres electrònics$2thub 615 0$aMeasure theory. 615 0$aProbabilities. 615 14$aMeasure and Integration. 615 24$aProbability Theory. 615 7$aTeoria de la mesura 615 7$aProbabilitats 676 $a515.42 700 $aGoswami$b Alok$01790997 701 $aRao$b B. V$01764417 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910986138703321 996 $aMeasure Theory for Analysis and Probability$94327855 997 $aUNINA