Book (Practical) Mathematics Integral and Functional Analysis, 2nd Edition / Tōru Maruyama

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Mathematics
[Introduction to Contents]
The theory of measures and integrals is one of the major cornerstones supporting modern analytical science. In this book, first, the basic matters are explained in detail along with the interface with functional analysis science. In addition, some special subjects of analytical science are described in detail, such as weak phases in the space of integrable functions and continuity of nonlinear integral operators defined in the space of integrable functions.
Contents
Part 1 Measures and Integrals
Measures
Measurable functions
Integrals
Integrals as measures
Integrals
Integrals as measures
Integrals
Integrals on Rl
Part 2 Function Space
Space of integrable functions, weak compactness in L1
Continuity of non-linear integral functions in L1
Duality in continuous function space and continuity of non-linear integral functions in L1
Preparation from Mathematics
Duality in continuous function space and * Weak convergence
Bochner Integrals
Vectors measure
Preparation from Mathematics
Duality in continuous function space and * Weak convergence
Bochner Integrals
Integrals in Multivalued Mapping
Convergence
Convergence
Continuous functions
Integrals in Multivalued Mapping
Theorem of Many-valued Mapping
Theorem of Urysohn
Compact
Continuity of Multivalued Mapping
Convergence
Continuous functions <