Real and functional analysis. 2nd ed. Part A: Real analysis

zbMath0641.46001MaRDI QIDQ1100680

B. George

Publication date: 1984

Published in: Mathematical Concepts and Methods in Science and Engineering (Search for Journal in Brave)

zbMATH Keywords

fixed point theoremsmeasurable functionschange of variablesproduct measuresLebesgue measuresigned measuresinner measureRadon-Nikodym theoremDaniell integralabsolutely continuous functionsStone-Weierstrass theoremFubini's theoremAscoli theoremabsolutely continuous measuresouter measuresBorel and Baire setsdifferentiation of real-valued functionsintegration versus differentiationnon-Lebesgue-measurable setsRiesz representation theorems

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Contents, measures, outer measures, capacities (28A12) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Integration with respect to measures and other set functions (28A25) Measures and integrals in product spaces (28A35) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis (46-01) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration (28-01) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15) Abstract differentiation theory, differentiation of set functions (28A15) Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures (28C05)

Related Items (15)

Global existence of solutions of the Boltzmann equation for Bose-Einstein particles with anisotropic initial data ⋮ Characterizing best isotone approximations in \(L_p\) spaces, \(1 \leq p < \infty\) ⋮ First eigenvalue of the \(p\)-Laplace operator along the Ricci flow ⋮ Supports of measure solutions for spatially homogeneous Boltzmann equations ⋮ Generalized Carathéodory extension theorem on fuzzy measure space ⋮ Variation of the first eigenvalue of Witten Laplacian and consequences under super Perelman-Ricci flow ⋮ Differential equations of divergence form in Musielak-Sobolev spaces and a sub-supersolution method ⋮ Drop properties and approximative compactness in Orlicz--Bochner function spaces ⋮ Monotonicity of eigenvalues of geometric operators along the Ricci-Bourguignon flow ⋮ The number of solutions for a class of nonlocal nonhomogeneous gradient operator equations ⋮ A result on uniqueness of mild solutions of Boltzmann equations ⋮ Surjectivity of isometries between weighted spaces of holomorphic functions ⋮ The first eigenvalue of Witten-Laplacian on manifolds with time-dependent metrics ⋮ Global existence and stability of solutions of spatially homogeneous Boltzmann equation for Fermi-Dirac particles ⋮ Invariant (fractal) vector measures as fixed points of Markov-type operators

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