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This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Mathematics. --- Functional analysis. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Measure theory. --- Probabilities. --- Functional Analysis. --- Global Analysis and Analysis on Manifolds. --- Measure and Integration. --- Probability Theory and Stochastic Processes. --- Vector spaces. --- Linear spaces --- Linear vector spaces --- Algebras, Linear --- Functional analysis --- Vector analysis --- Global analysis. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Math --- Science --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic
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This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Differential geometry. Global analysis --- Functional analysis --- Operational research. Game theory --- Probability theory --- Mathematics --- Mathematical physics --- differentiaalvergelijkingen --- topologie (wiskunde) --- waarschijnlijkheidstheorie --- stochastische analyse --- functies (wiskunde) --- statistiek --- wiskunde --- kansrekening
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