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Lebesgue integral. --- Integration, Lebesgue --- L-integral --- Lebesgue integration --- Lebesgue-Stieltjes integral --- Lebesgue's integral --- Stieltjes integral, Lebesgue --- -Integrals, Generalized --- Measure theory --- Integral de Lebesgue --- Integrals generalitzades --- Teoria de la mesura
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This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.
Funcions de variables reals --- Teoria de la mesura --- Anells (Àlgebra) --- Integrals generalitzades --- Integral de Lebesgue --- Teoria ergòdica --- Teoria de la mesura geomètrica --- Àlgebres de mesura --- Variables reals --- Funcions còncaves --- Funcions de diverses variables reals --- Funcions de variables complexes --- Functions of real variables. --- Measure theory. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Real variables --- Functions of complex variables --- Mathematics. --- Math --- Science
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Documents the rich structure of the holomorphic Q function spaces which are geometric in the sense that they transform naturally under conformal mappings, with particular emphasis on the development based on interaction between geometric function and measure theory and other branches of mathematical analysis.
Integration, Functional. --- Functions of complex variables. --- Holomorphic functions. --- Intégration des fonctions --- Fonctions d'une variable complexe --- Fonctions holomorphes --- Integration, Functional --- Functions of complex variables --- Holomorphic functions --- Calculus --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Functions, Holomorphic --- Complex variables --- Functional integration --- Mathematics. --- Geometry. --- Elliptic functions --- Functions of real variables --- Functional analysis --- Integrals, Generalized --- Functions of several complex variables --- Euclid's Elements --- Integral de Lebesgue --- Funcions de variables complexes --- Funcions holomorfes --- Funcions de diverses variables complexes --- Anàlisi complexa --- Funció d'una variable complexa --- Variables complexes --- Aplicacions quasiconformes --- Funcions abelianes --- Funcions analítiques --- Funcions convexes --- Funcions enteres --- Funcions meromorfes --- Funcions univalents --- Grups discontinus --- Invariants conformes --- Problemes de contorn --- Sèries de Lie --- Teoria geomètrica de funcions --- Funcions de variables reals --- Funcions el·líptiques --- Sistemes dinàmics complexos --- Integrals generalitzades --- Teoria de la mesura
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Equacions diferencials --- Anàlisi funcional --- Teoria de la mesura --- Anells (Àlgebra) --- Integrals generalitzades --- Integral de Lebesgue --- Teoria ergòdica --- Teoria de la mesura geomètrica --- Àlgebres de mesura --- Càlcul funcional --- Càlcul de variacions --- Àlgebres de Hilbert --- Àlgebres topològiques --- Anàlisi funcional no lineal --- Anàlisi microlocal --- Espais analítics --- Espais de Hardy --- Espais d'Orlicz --- Espais funcionals --- Espais vectorials normats --- Espais vectorials --- Filtres digitals (Matemàtica) --- Funcionals --- Funcions vectorials --- Multiplicadors (Anàlisi matemàtica) --- Pertorbació (Matemàtica) --- Teoria d'operadors --- Teoria de distribucions (Anàlisi funcional) --- Teoria de functors --- Teoria de l'aproximació --- Teoria del funcional de densitat --- Teoria espectral (Matemàtica) --- Equacions funcionals --- Equacions integrals --- Càlcul --- Funcions de Bessel --- Àlgebra diferencial --- Càlcul integral --- Càlcul operacional --- Equacions d'evolució --- Equacions de camp d'Einstein --- Equacions de Lagrange --- Equacions de Pfaff --- Equacions diferencials algebraiques --- Equacions diferencials ordinàries --- Equacions en derivades parcials --- Funcions de Green --- Funcions de Lyapunov --- Problemes de contorn --- Problemes inversos (Equacions diferencials) --- Teoria d'estabilitat (Matemàtica) --- Transformació de Laplace --- Differential equations. --- 517.91 Differential equations --- Differential equations
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This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed.
Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Measure theory. --- Analysis. --- Functional Analysis. --- Measure and Integration. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Anàlisi matemàtica --- Anàlisi funcional --- Teoria de la mesura --- Anells (Àlgebra) --- Integrals generalitzades --- Integral de Lebesgue --- Teoria ergòdica --- Teoria de la mesura geomètrica --- Àlgebres de mesura --- Càlcul funcional --- Càlcul de variacions --- Àlgebres de Hilbert --- Àlgebres topològiques --- Anàlisi funcional no lineal --- Anàlisi microlocal --- Espais analítics --- Espais de Hardy --- Espais d'Orlicz --- Espais funcionals --- Espais vectorials normats --- Espais vectorials --- Filtres digitals (Matemàtica) --- Funcionals --- Funcions vectorials --- Multiplicadors (Anàlisi matemàtica) --- Pertorbació (Matemàtica) --- Teoria d'operadors --- Teoria de distribucions (Anàlisi funcional) --- Teoria de functors --- Teoria de l'aproximació --- Teoria del funcional de densitat --- Teoria espectral (Matemàtica) --- Equacions funcionals --- Equacions integrals --- Matemàtica --- Àlgebra lineal --- Anàlisi combinatòria --- Anàlisi de Fourier --- Anàlisi estocàstica --- Anàlisi matemàtica no-estàndard --- Anàlisi numèrica --- Funcions --- Matemàtica per a enginyers --- Sèries infinites --- Teoria del potencial (Matemàtica) --- Teories no lineals --- Rutes aleatòries (Matemàtica) --- Àlgebra --- Càlcul --- Evolution equations. --- Evolutionary equations --- Equations, Evolution --- Equations of evolution --- Differential equations
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Measure theory. --- Probabilities. --- Stochastic processes. --- Random processes --- Probabilities --- 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) --- Teoria de la mesura --- Probabilitats --- Processos estocàstics --- Càlcul estocàstic --- Funcions aleatòries --- Processos aleatoris --- Anàlisi estocàstica --- Aproximació estocàstica --- Camps aleatoris --- Filtre de Kalman --- Fluctuacions (Física) --- Martingales (Matemàtica) --- Mètode de Montecarlo --- Processos de Markov --- Processos de ramificació --- Processos gaussians --- Processos puntuals --- Rutes aleatòries (Matemàtica) --- Semimartingales (Matemàtica) --- Sistemes estocàstics --- Teoremes de límit (Teoria de probabilitats) --- Teoria de cues --- Teoria de l'estimació --- Teoria de la predicció --- Càlcul de probabilitats --- Inferència estadística --- Probabilitat --- Combinatòria (Matemàtica) --- Lògica --- Lògica matemàtica --- Anàlisi de sèries temporals --- Correlació (Estadística) --- Descomposició (Matemàtica) --- Distribució (Teoria de la probabilitat) --- Fiabilitat (Enginyeria) --- Funcions característiques --- Geometria estocàstica --- Incertesa (Teoria de la informació) --- Integrals de camí --- Jocs d'atzar (Matemàtica) --- Mitjana (Estadística) --- Probabilitats combinatòries --- Sort --- Teoria matemàtica de la comunicació --- Variables aleatòries --- Atzar --- Risc (Economia) --- Teoria ergòdica --- Anells (Àlgebra) --- Integrals generalitzades --- Integral de Lebesgue --- Teoria de la mesura geomètrica --- Àlgebres de mesura
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