{"product_id":"dual-of-linfinityxl-finitely-additive-measures-and-weak-convergence-9783030347321","title":"Dual of Linfinity(X,L,?), Finitely Additive Measures and Weak Convergence","description":"\u003cp\u003eIn measure theory, a familiar representation theorem due to F. Riesz identifies the dual space Lp(X,L,λ)* with Lq(X,L,λ), where 1\/p+1\/q=1, as long as 1 ≤ p\u0026lt;∞. However, L∞(X,L,λ)* cannot be similarly described, and is instead represented as a class of finitely additive measures. This book provides a reasonably elementary account of the representation theory of L∞(X,L,λ)*, examining pathologies and paradoxes, and uncovering some surprising consequences. For instance, a necessary and sufficient condition for a bounded sequence in L∞(X,L,λ) to be weakly convergent, applicable in the one-point compactification of X, is given. With a clear summary of prerequisites, and illustrated by examples including L∞(Rn) and the sequence space l∞, 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":"Gardners","offers":[{"title":"Default Title","offer_id":52915584565527,"sku":null,"price":7422.41,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030347321.jpg?v=1781527356","url":"https:\/\/payment.letskitaboo.com\/ur\/products\/dual-of-linfinityxl-finitely-additive-measures-and-weak-convergence-9783030347321","provider":"Kitaboo One eStore","version":"1.0","type":"link"}