{"product_id":"9783030347314","title":"SpringerBriefs in Mathematics: A Primer","description":"\u003ch1\u003eSpringerBriefs in Mathematics: A Primer\u003c\/h1\u003e \u003ch2\u003eToland, John\u003c\/h2\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 ≤ p\u0026lt;∞. However, \u003ci\u003eL\u003c\/i\u003e\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 \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2020-02-07\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030347314\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-34732-1\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 99\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45548656328844,"sku":"9783030347314","price":62.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030347314.jpg?v=1775785915","url":"https:\/\/lateknightbooks.com\/products\/9783030347314","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}