Infinite Dimensional Analysis: A Hitchhiker's Guide, Third Edition This book provides a comprehensive introduction to infinite dimensional analysis, covering topics such as topology, measure theory, functional analysis, and convex analysis. It is designed for graduate students and researchers in economics, mathematics, and related fields. The book includes a detailed treatment of convex sets and functions, as well as a new chapter on convex analysis. It also includes a discussion of measurable correspondences, which are essential in economic theory. The book is structured into 19 chapters, each covering a specific topic in infinite dimensional analysis. The first chapter introduces basic concepts such as numbers, sets, relations, and functions. The second chapter discusses topology, including topological spaces, continuity, compactness, and convergence. The third chapter covers metrizable spaces, including metric spaces, completeness, and uniform continuity. The fourth chapter discusses measurability, including algebras of sets, measurable functions, and product structures. The fifth chapter introduces topological vector spaces, including linear topologies, metrizable spaces, and the Open Mapping and Closed Graph Theorems. The sixth chapter discusses normed spaces, including Banach spaces, linear operators, and the uniform boundedness principle. The seventh chapter focuses on convexity, including convex sets, support points, subgradients, and convex functions. The eighth chapter discusses Riesz spaces, including orders, lattices, and cones. The ninth chapter covers Banach lattices, including Fréchet and Banach lattices, the Stone-Weierstrass Theorem, and order continuous norms. The tenth chapter discusses charges and measures, including set functions, outer measures, and the Carathéodory extension of a measure. The eleventh chapter covers integrals, including the Lebesgue integral, the Riemann integral, and the Bochner integral. The twelfth chapter discusses measures and topology, including Borel measures, regularity, and the Choquet Capacity Theorem. The thirteenth chapter covers Lp-spaces, including norms, inequalities, and duals of Lp-spaces. The fourteenth chapter discusses Riesz Representation Theorems, including the dual of Cb(X) and the dual of Cc(X). The fifteenth chapter covers probability measures, including the weak* topology on P(X), and the Kolmogorov Extension Theorem. The sixteenth chapter discusses spaces of sequences, including sequence spaces, the space of convergent sequences, and the space of sequences with only finitely many nonzero terms. The seventeenth chapter discusses correspondences, including continuity, hemicontinuity, and fixed point theorems. The eighteenth chapter discusses measurable correspondences, including measurability, compact-valued correspondences, and measurable selectors. The nineteenth chapter discusses Markov transitions, including Markov operators, invariant measures, and ergodic measures. The twentieth chapter discusses ergodicInfinite Dimensional Analysis: A Hitchhiker's Guide, Third Edition This book provides a comprehensive introduction to infinite dimensional analysis, covering topics such as topology, measure theory, functional analysis, and convex analysis. It is designed for graduate students and researchers in economics, mathematics, and related fields. The book includes a detailed treatment of convex sets and functions, as well as a new chapter on convex analysis. It also includes a discussion of measurable correspondences, which are essential in economic theory. The book is structured into 19 chapters, each covering a specific topic in infinite dimensional analysis. The first chapter introduces basic concepts such as numbers, sets, relations, and functions. The second chapter discusses topology, including topological spaces, continuity, compactness, and convergence. The third chapter covers metrizable spaces, including metric spaces, completeness, and uniform continuity. The fourth chapter discusses measurability, including algebras of sets, measurable functions, and product structures. The fifth chapter introduces topological vector spaces, including linear topologies, metrizable spaces, and the Open Mapping and Closed Graph Theorems. The sixth chapter discusses normed spaces, including Banach spaces, linear operators, and the uniform boundedness principle. The seventh chapter focuses on convexity, including convex sets, support points, subgradients, and convex functions. The eighth chapter discusses Riesz spaces, including orders, lattices, and cones. The ninth chapter covers Banach lattices, including Fréchet and Banach lattices, the Stone-Weierstrass Theorem, and order continuous norms. The tenth chapter discusses charges and measures, including set functions, outer measures, and the Carathéodory extension of a measure. The eleventh chapter covers integrals, including the Lebesgue integral, the Riemann integral, and the Bochner integral. The twelfth chapter discusses measures and topology, including Borel measures, regularity, and the Choquet Capacity Theorem. The thirteenth chapter covers Lp-spaces, including norms, inequalities, and duals of Lp-spaces. The fourteenth chapter discusses Riesz Representation Theorems, including the dual of Cb(X) and the dual of Cc(X). The fifteenth chapter covers probability measures, including the weak* topology on P(X), and the Kolmogorov Extension Theorem. The sixteenth chapter discusses spaces of sequences, including sequence spaces, the space of convergent sequences, and the space of sequences with only finitely many nonzero terms. The seventeenth chapter discusses correspondences, including continuity, hemicontinuity, and fixed point theorems. The eighteenth chapter discusses measurable correspondences, including measurability, compact-valued correspondences, and measurable selectors. The nineteenth chapter discusses Markov transitions, including Markov operators, invariant measures, and ergodic measures. The twentieth chapter discusses ergodic