Measures, Integrals and MartingalesCambridge University Press, 10.11.2005 This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability theory. The basic theory - measures, integrals, convergence theorems, Lp-spaces and multiple integrals - is explored in the first part of the book. The second part then uses the notion of martingales to develop the theory further, covering topics such as Jacobi's generalized transformation Theorem, the Radon-Nikodym theorem, Hardy-Littlewood maximal functions or general Fourier series. Undergraduate calculus and an introductory course on rigorous analysis are the only essential prerequisites, making this text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included and these are not merely drill problems but are there to consolidate what has already been learnt and to discover variants, sideways and extensions to the main material. Hints and solutions can be found on the author's website, which can be reached from www.cambridge.org/9780521615259. This book forms a sister volume to René Schilling's other book Counterexamples in Measure and Integration (www.cambridge.org/9781009001625). |
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analytic sets assume axiom of choice Borel set bounded function closed sets compact set continuous function Corollary countable intersection d x y Definition Let denoted dense detD differential calculus equivalence class f is continuous functions on a b h t z Hausdorff space improper integrals Improper Riemann integrals inequality j→lim j>k j>k Lebesgue integral Lebesgue measurable sets Let u a b lim inf lim sup limit lim limj mean value theorem metric space n→lim normed space numbers open neighbourhood open sets partition of a b pathwise connected primitive Proof of Theorem resp sequence xj shows Souslin scheme step functions subset supV a b Theorem E.8 Theorem Let theorem of differential topological space topology u t dt u t v t dt u t y dt ΚΕΝ
Verweise auf dieses Buch
Pseudo Differential Operators & Markov Processes: Markov processes and ... Niels Jacob Eingeschränkte Leseprobe - 2001 |