W SWARTZ C (EN) — MEASURE, INTEGRATION AND FUNCTION SPACES

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MEASURE, INTEGRATION AND FUNCTION SPACES
Язык книги: Английский
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This text contains a basic introduction to the abstract measure theory and the Lebesgue integral. Most of the standard topics in the measure and integration theory are discussed. In addition, topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions not contained in standard texts are explored. There is an introductory section on functional analysis, including the three basic principles, which is used to discuss many of the classic Banach spaces of functions and their duals. There is also a chapter on Hilbert space and the Fourier transform.Contents:Measure Theory:Lebesgue MeasureLebesgue-Stieltjes MeasureThe Nikodym Convergence and Boundedness TheoremsIntegration:Measurable FunctionsThe Lebesgue Integral Convergence in MeanConvergence in MeasureComparison of Modes of ConvergenceThe Radon-Nikodym TheoremThe Vitali-Hahn-Saks TheoremDifferentiation and Integration:Integrating DerivativesAbsolutely Continuous FunctionsIntroduction to Functional Analysis:Normed Linear Spaces (NLS)Quotient SpacesThe Hahn-Banach TheoremOrdered Linear SpacesFunction Spaces:Lp-Spaces, 1 ≤ p < ∞The Space of Finitely Additive Set FunctionsThe Space of Countably Additive Set FunctionsThe Space of Continuous FunctionsHilbert Spaceand other papersReadership: Mathematicians and graduate students in mathematics.Key Features:Describes the major demographic, socio-economic, and institutional drivers for change in East AsiaProvides important facts on the variability of the East Asian monsoon over the last several million yearsShows that models are capable of reproducing past variations in climate and that they will be useful for evaluating future changes in land use and climatePortrays what the region will be like in 50 years' timeConsiders the impact of deforestation, construction of dams, and domestic and industrial use of water on sediment and nutrient delivery to coastal zones and its effect on species diversity, benthic biomass and fish resources

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MEASURE, INTEGRATION AND FUNCTION SPACES - читать книгу онлайн бесплатно, автор W SWARTZ C (EN)

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