{"product_id":"measure-theory-and-integration-9780821887189","title":"Measure Theory and Integration","description":"\u003cp\u003e • Author(s): Michael E Taylor\u003cbr\u003e • Publisher: Orient Blackswan Pvt Ltd\u003cbr\u003e • Publisher Imprint: Orient Blackswan Pvt Ltd\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis self-contained treatment of\u003cstrong\u003e measure and integration\u003c\/strong\u003e begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to \u003cem\u003eL\u003csup\u003ep\u003c\/sup\u003e\u003c\/em\u003e spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to \u003cem\u003eL\u003csup\u003e2\u003c\/sup\u003e\u003c\/em\u003e spaces as Hilbert spaces, with a useful geometrical structure.\u003c\/p\u003e \u003cp\u003eHaving gotten quickly to the heart of the matter, the text proceeds to broaden its scope. There are further constructions of measures, including Lebesgue measure on $n$-dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration of differential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales.\u003c\/p\u003e \u003cp\u003eThis text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory.\u003c\/p\u003e","brand":"Orient Blackswan Pvt Ltd","offers":[{"title":"Paperback","offer_id":45616519053463,"sku":"9780821887189","price":847.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780821887189.webp?v=1769295010","url":"https:\/\/atlanticbooks.com\/products\/measure-theory-and-integration-9780821887189","provider":"Atlantic Books","version":"1.0","type":"link"}