{"product_id":"the-dual-of-l-8734-x-l-955-finitely-additive-measures-and-weak-convergence-a-primer-9783030347314","title":"The Dual of L\u0026#8734;(x, L,\u0026#955;), Finitely Additive Measures and Weak Convergence: A Primer","description":"\u003cp\u003e • Author(s): John Toland\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Mathematical Analysis\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn measure theory, a familiar representation theorem due to F. Riesz identifies the dual space \u003ci\u003eL\u003c\/i\u003e\u003csub\u003ep\u003c\/sub\u003e(X, L,λ)* with \u003ci\u003eL\u003c\/i\u003e\u003csub\u003eq\u003c\/sub\u003e(X, L,λ), where 1\/p+1\/q=1, as long as 1 L\u003csub\u003e∞\u003c\/sub\u003e(X, L,λ)* cannot be similarly described, and is instead represented as a class of finitely additive measures.\u003c\/p\u003e\u003cp\u003eThis book provides a reasonably elementary account of the representation theory of \u003ci\u003eL\u003c\/i\u003e\u003csub\u003e∞\u003c\/sub\u003e(X, L,λ)*, examining pathologies and paradoxes, and uncovering some surprising consequences. For instance, a necessary and sufficient condition for a bounded sequence in \u003ci\u003eL\u003c\/i\u003e\u003csub\u003e∞\u003c\/sub\u003e(X, L,λ) to be weakly convergent, applicable in the one-point compactification of X, is given.\u003c\/p\u003e\u003cp\u003eWith a clear summary of prerequisites, and illustrated by examples including \u003ci\u003eL\u003c\/i\u003e\u003csub\u003e∞\u003c\/sub\u003e(\u003cb\u003eR\u003c\/b\u003e\u003csup\u003en\u003c\/sup\u003e) and the sequence space \u003ci\u003el\u003c\/i\u003e\u003csub\u003e∞\u003c\/sub\u003e, this book makes possibly unfamiliar material, some of which may be new, accessible to students and researchers in the mathematical sciences.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45280340738199,"sku":"9783030347314","price":4774.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783030347314.webp?v=1769296046","url":"https:\/\/atlanticbooks.com\/products\/the-dual-of-l-8734-x-l-955-finitely-additive-measures-and-weak-convergence-a-primer-9783030347314","provider":"Atlantic Books","version":"1.0","type":"link"}