This book, titled "Convex Analysis and Measurable Multifunctions," is part of the Lecture Notes in Mathematics series, edited by A. Dold and B. Eckmann, and authored by Charles Castaing and Michel Valadier. It was published by Springer-Verlag in 1977. The book covers convex analysis, measurable multifunctions, and their applications. It assumes a good understanding of analysis, with references to Bourbaki or Dunford-Schwartz as suitable textbooks. The authors acknowledge that some topics, such as the Borel selection theorem and set-valued measures, are not treated in detail but provide references for further study. Each chapter includes a bibliography, and the preface expresses gratitude to colleagues and staff who contributed to the manuscript. The content is divided into eight chapters, each focusing on specific aspects of convex functions, Hausdorff distance, measurable multifunctions, compactness theorems, primitive multifunctions, convex integrands, and natural supplements of \(L^1\) in the dual of \(L^\infty\). The book also includes a subject index for easy reference.This book, titled "Convex Analysis and Measurable Multifunctions," is part of the Lecture Notes in Mathematics series, edited by A. Dold and B. Eckmann, and authored by Charles Castaing and Michel Valadier. It was published by Springer-Verlag in 1977. The book covers convex analysis, measurable multifunctions, and their applications. It assumes a good understanding of analysis, with references to Bourbaki or Dunford-Schwartz as suitable textbooks. The authors acknowledge that some topics, such as the Borel selection theorem and set-valued measures, are not treated in detail but provide references for further study. Each chapter includes a bibliography, and the preface expresses gratitude to colleagues and staff who contributed to the manuscript. The content is divided into eight chapters, each focusing on specific aspects of convex functions, Hausdorff distance, measurable multifunctions, compactness theorems, primitive multifunctions, convex integrands, and natural supplements of \(L^1\) in the dual of \(L^\infty\). The book also includes a subject index for easy reference.