03985nam 22005175 450 991103167180332120251001130603.0981-9527-58-910.1007/978-981-95-2758-8(CKB)41521165200041(MiAaPQ)EBC32324975(Au-PeEL)EBL32324975(DE-He213)978-981-95-2758-8(EXLCZ)994152116520004120251001d2025 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierElements of Measure and Probability /by Arup Bose1st ed. 2025.Singapore :Springer Nature Singapore :Imprint: Springer,2025.1 online resource (318 pages)Texts and Readings in Mathematics,2366-8725 ;88981-9527-57-0 Preliminaries -- Classes of Sets -- Introduction to Measures -- Extension of Measures -- Lebesgue-Stieltjes Measures -- Measurable Functions -- Integral -- Basic Inequalities -- Lp Spaces: Topological Properties -- Product Spaces and Transition Measures -- Random Variables and Vectors -- Moments and Cumulants -- Further Modes of Convergence of Functions -- Independence and Basic Conditional Probability -- 0-1 Laws -- Sums of Independent Random Variables -- Convergence of Finite Measures -- Characteristic Functions -- Central Limit Theorem -- Signed Measure -- Randon-Nikodym Theorem -- Fundamental Theorem of Calculus -- Conditional Expectation.This book can serve as a first course on measure theory and measure theoretic probability for upper undergraduate and graduate students of mathematics, statistics and probability. Starting from the basics, the measure theory part covers Caratheodory’s theorem, Lebesgue–Stieltjes measures, integration theory, Fatou’s lemma, dominated convergence theorem, basics of Lp spaces, transition and product measures, Fubini’s theorem, construction of the Lebesgue measure in Rd, convergence of finite measures, Jordan–Hahn decomposition of signed measures, Radon–Nikodym theorem and the fundamental theorem of calculus. The material on probability covers standard topics such as Borel–Cantelli lemmas, behaviour of sums of independent random variables, 0-1 laws, weak convergence of probability distributions, in particular via moments and cumulants, and the central limit theorem (via characteristic function, and also via cumulants), and ends with conditional expectation as a natural application of the Radon–Nikodym theorem. A unique feature is the discussion of the relation between moments and cumulants, leading to Isserlis’ formula for moments of products of Gaussian variables and a proof of the central limit theorem avoiding the use of characteristic functions. For clarity, the material is divided into 23 (mostly) short chapters. At the appearance of any new concept, adequate exercises are provided to strengthen it. Additional exercises are provided at the end of almost every chapter. A few results have been stated due to their importance, but their proofs do not belong to a first course. A reasonable familiarity with real analysis is needed, especially for the measure theory part. Having a background in basic probability would be helpful, but we do not assume a prior exposure to probability.Texts and Readings in Mathematics,2366-8725 ;88Measure theoryProbabilitiesMeasure and IntegrationProbability TheoryMeasure theory.Probabilities.Measure and Integration.Probability Theory.515.42Bose Arup768007MiAaPQMiAaPQMiAaPQBOOK9911031671803321Elements of Measure and Probability4443102UNINA06813nam 2200913 a 450 991096007960332120251017110053.09786610193486978128019348412801934849780309593144030959314X97805850531340585053138(CKB)110986584751448(EBL)3377839(SSID)ssj0000228012(PQKBManifestationID)12085140(PQKBTitleCode)TC0000228012(PQKBWorkID)10141797(PQKB)11272729(MiAaPQ)EBC3377839(Au-PeEL)EBL3377839(CaPaEBR)ebr10075672(CaONFJC)MIL19348(OCoLC)923273498(DNLM)786899(BIP)1294261(EXLCZ)9911098658475144819940815d1994 uy 0engur|n|---|||||txtccrProceedings Workshop on Needle Exchange and Bleach Distribution Programs /Panel on Needle Exchange and Bleach Distribution Programs, Commission on Behavioral and Social Sciences and Education, National Research Council and Institute of Medicine1st ed.Washington, DC National Academy Press19941 online resource (320 p.)Project was sponsored by the National Institute on Drug Abuse.Workshop was held on September 27-28, 1993 in Baltimore, Maryland.Panel chairman: Lincoln Moses.Print version: Staff, National Research Council. Workshop on Needle Exchange and Bleach Distribution Programs Proceedings. Washington : National Academies Press, ©1993 9780309050845 Includes bibliographical references.""Proceedings Workshop on Needle Exchange and Bleach Distribution Programs""; ""Copyright""; ""Contents""; ""PREFACE""; ""INTRODUCTION""; ""REFERENCES""; ""U.S. NEEDLE EXCHANGE DATA""; ""The University of California Needle Exchange Program Evaluation Project: Methods, Conclusions, and Recommendation ""; ""METHODS""; ""Project Personnel""; ""Goal and Research Questions""; ""Ensuring Community and Expert Input""; ""Advisory Committee""; ""Expert Reviewers""; ""Kaiser Family Foundation Forum""; ""Consent and Confidentiality""; ""Formal Review of Existing Research""; ""Assessment of Data Needs""""Data Collection""""Data Synthesis""; ""Site Visits""; ""Identification of Sites and Interviewees""; ""Methodological Framework""; ""Training""; ""Site Observations""; ""Key Informant Interviews""; ""IDU Focus Groups""; ""Qualitative Analysis""; ""Mail Survey of NEPs Not Visited""; ""Cost-Effectiveness Modeling""; ""CONCLUSIONS""; ""How and Why Did NEPs Develop?""; ""How Do NEPs Operate?""; ""Do NEPs Act as Bridges to Public Health Services?""; ""How Much Does it Cost to Operate NEPs?""; ""Who Are the IDUs Who Use NEPs?""; ""What Proportion of All IDUs in a Community Uses the NEP?""""What Are the Community Responses to NEPs?""""Do NEPs Result in Changes in Community Levels of Drug Use?""; ""Do NEPs Affect the Number of Discarded Syringes?""; ""Do NEPs Affect Rates of HIV Drug and/or Sex Risk Behaviors?""; ""What is the Role of Studies of Syringes in Injection Drug Use Research?""; ""Do NEPs Affect Rates of Diseases Related to Injection Drug Use Other than HIV?""; ""Do NEPs Affect HIV Infection Rates?""; ""Are NEPs Cost-effective in Preventing HIV Infection?""; ""RECOMMENDATIONS""; ""Recommendations for the Federal Government""; ""Recommendations for State Governments""""Recommendations for Researchers""""APPENDIX""; ""Research Questions""; ""References""; ""Risk for Human Immunodeficiency Virus and Hepatitis B Virus in Users of the Tacoma Syringe Exchange Program""; ""INTRODUCTION""; ""METHODS""; ""The Intervention""; ""Studies of Risk Behavior in Local IDUs""; ""Surveillance of Blood-Borne Viral Infections""; ""Case-Control Study of Incident HBV Infections""; ""RESULTS""; ""DISCUSSIONS""; ""References""; ""Behavioral and Community Impact of the Portland Syringe Exchange Program""; ""PROGRAM OVERVIEW""; ""METHODS""; ""RESULTS""; ""CONCLUSIONS""""ACKNOWLEDGMENTS""""Reference""; ""New York City Syringe Exchange: An Overview""; ""INTRODUCTION""; ""OVERVIEW OF EVALUATION""; ""METHODS""; ""Ethnographic Study""; ""Behavioral Change and Seroconversion""; ""Seroprevalence and Seroincidence""; ""RESULTS""; ""Organizational-System Issues""; ""Health Departments""; ""The American Foundation for AIDS Research (AmFAR)""; ""Syringe Exchange Programs""; ""Evaluation""; ""PROBLEM SOLVING""; ""Subject Characteristics""; ""Self-Reported Change in Risk-Taking Behavior""; ""DISCUSSION""; ""ACKNOWLEDGMENTS""; ""References""""Discussion: U.S. Needle Exchange Data""This book reports on research on and experience with needle exchange and bleach distribution programs and their effects on rates of drug use, the behavior of injection drug users, and the spread of HIV and other infectious diseases among injection drug users. It discusses U.S. needle exchange data, international evaluations of needle exchange programs, legal issues and drug paraphernalia laws, evaluation methods, and bleach distribution programs.Needle exchange programsUnited StatesIntravenous drug abuseHealth aspectsUnited StatesAIDS (Disease)United StatesPreventionChlorine and derivatives as disinfectantsHIV Infectionsprevention & controlNeedle-Exchange Programsorganization & administrationDisinfectantssupply & distributionConference Proceedings.Needle exchange programsIntravenous drug abuseHealth aspectsAIDS (Disease)Prevention.Chlorine and derivatives as disinfectants.HIV Infectionsprevention & control.Needle-Exchange Programsorganization & administration.Disinfectantssupply & distribution.362.29Moses Lincoln E103130National Research Council (U.S.).Panel on Needle Exchange and Bleach Distribution Programs.National Research Council (U.S.).Commission on Behavioral and Social Sciences and Education.Institute of Medicine (U.S.)Workshop on Needle Exchange and Bleach Distribution ProgramsMiAaPQMiAaPQMiAaPQBOOK9910960079603321Proceedings4341394UNINA