{"product_id":"the-dual-of-l8x-l-finitely-additive-measures-and-weak-convergence-a-primer-von-john-toland","title":"The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence","description":"\n                                \n                \u003cp\u003e\n                                        In measure theory, a familiar representation theorem due to F. Riesz identifies the dual space \n                    \n                    \u003ci\u003eL\u003c\/i\u003e\n                                        \n                    \u003csub\u003ep\u003c\/sub\u003e\n                                        (X,L,λ)*  with \n                    \n                    \u003ci\u003eL\u003c\/i\u003e\n                                        \n                    \u003csub\u003eq\u003c\/sub\u003e\n                                        (X,L,λ), where 1\/p+1\/q=1, as long as 1 ≤ p\u0026lt;∞. However, \n                    \n                    \u003ci\u003eL\u003c\/i\u003e\n                                        \n                    \u003csub\u003e∞\u003c\/sub\u003e\n                                        (X,L,λ)* cannot be similarly described, and is instead represented as a class of finitely additive measures.\n                \n                \u003c\/p\u003e\n                                \n                \u003cp\u003e\n                                        This book provides a reasonably elementary account of the representation theory of \n                    \n                    \u003ci\u003eL\u003c\/i\u003e\n                                        \n                    \u003csub\u003e∞\u003c\/sub\u003e\n                                        (X,L,λ)*, examining pathologies and paradoxes, and uncovering some surprising consequences. For instance, a necessary and sufficient condition for a bounded sequence in \n                    \n                    \u003ci\u003eL\u003c\/i\u003e\n                                        \n                    \u003csub\u003e∞\u003c\/sub\u003e\n                                        (X,L,λ) to be weakly convergent, applicable in the one-point compactification of X, is given.\n                \n                \u003c\/p\u003e\n                                \n                \u003cp\u003e\n                                        With a clear summary of  prerequisites, and illustrated by examples including \n                    \n                    \u003ci\u003eL\u003c\/i\u003e\n                                        \n                    \u003csub\u003e∞\u003c\/sub\u003e\n                                        (\n                    \n                    \u003cb\u003eR\u003c\/b\u003e\n                                        \n                    \u003csup\u003en\u003c\/sup\u003e\n                                        ) and the sequence space \n                    \n                    \u003ci\u003el\u003c\/i\u003e\n                                        \n                    \u003csub\u003e∞\u003c\/sub\u003e\n                                        , this book makes possibly unfamiliar material, some of which may be new, accessible to students and researchers in the mathematical sciences.\n                \n                \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783030347314\"\u003e\u003ch3\u003eA Primer\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783030347314","offer_id":39424163283037,"sku":"9783030347314","price":69.54,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/43a577ac-fb92-4478-aadc-b8d8e6ed12f5.jpg?v=1772170446","url":"https:\/\/shop.autorenwelt.de\/products\/the-dual-of-l8x-l-finitely-additive-measures-and-weak-convergence-a-primer-von-john-toland","provider":"Autorenwelt Shop","version":"1.0","type":"link"}