Matches in SemOpenAlex for { <https://semopenalex.org/work/W2055165045> ?p ?o ?g. }
- W2055165045 endingPage "238" @default.
- W2055165045 startingPage "206" @default.
- W2055165045 abstract "There are a number of important analytical situations in which the approach to an integral through a measure space is unnatural or technically disadvantageous. In fact, we have developed a major part of the theory from the point of view of integration lattices, following the fundamental ideas of Daniell. However, in the examples of integration lattices considered so far, e.g., the real step functions on a basic measure space or the continuous real-valued functions of compact support on a locally compact space, there is another inherent element of structure which in many respects is more important; these particular lattices are also algebras, and there are definite advantages from a broad viewpoint to a formulation of integration theory which starts from a linear functional on an algebra rather than a lattice. This approach to the theory of integration, which might be called the algebraic approach, is not restricted to function algebras alone, arises naturally from the foundations of probability theory, and is explicitly or implicitly indicated in a variety of other situations, e.g., commutative spectral theory in Hilbert space, the theory of integration in infinite-dimensional linear spaces, harmonic analysis on Abelian and more general groups (in particular, the L2 theory), and developments closely paralleling integration theory in the theory of rings of operators." @default.
- W2055165045 created "2016-06-24" @default.
- W2055165045 creator A5028049625 @default.
- W2055165045 date "1978-01-01" @default.
- W2055165045 modified "2023-09-24" @default.
- W2055165045 title "Algebraic Integration Theory" @default.
- W2055165045 cites W1504779208 @default.
- W2055165045 cites W1518430783 @default.
- W2055165045 cites W1520187819 @default.
- W2055165045 cites W1530330303 @default.
- W2055165045 cites W1532803486 @default.
- W2055165045 cites W1533684288 @default.
- W2055165045 cites W1538859014 @default.
- W2055165045 cites W1539619731 @default.
- W2055165045 cites W1541074945 @default.
- W2055165045 cites W1542786224 @default.
- W2055165045 cites W1543224718 @default.
- W2055165045 cites W1547322272 @default.
- W2055165045 cites W1586915582 @default.
- W2055165045 cites W1945843680 @default.
- W2055165045 cites W1964379255 @default.
- W2055165045 cites W1964917948 @default.
- W2055165045 cites W1969106030 @default.
- W2055165045 cites W1973053315 @default.
- W2055165045 cites W1978826851 @default.
- W2055165045 cites W1981479929 @default.
- W2055165045 cites W1988003560 @default.
- W2055165045 cites W1991200719 @default.
- W2055165045 cites W1995716794 @default.
- W2055165045 cites W1997093580 @default.
- W2055165045 cites W1999500263 @default.
- W2055165045 cites W2000243721 @default.
- W2055165045 cites W2001119194 @default.
- W2055165045 cites W2002976752 @default.
- W2055165045 cites W2004827106 @default.
- W2055165045 cites W2005200870 @default.
- W2055165045 cites W2008330486 @default.
- W2055165045 cites W2009786154 @default.
- W2055165045 cites W2012395494 @default.
- W2055165045 cites W2015227148 @default.
- W2055165045 cites W2015380592 @default.
- W2055165045 cites W2017096836 @default.
- W2055165045 cites W2018449147 @default.
- W2055165045 cites W2024089403 @default.
- W2055165045 cites W2025057664 @default.
- W2055165045 cites W2025094856 @default.
- W2055165045 cites W2026085959 @default.
- W2055165045 cites W2028604883 @default.
- W2055165045 cites W2031366935 @default.
- W2055165045 cites W2033422925 @default.
- W2055165045 cites W2034003144 @default.
- W2055165045 cites W2036636665 @default.
- W2055165045 cites W2037315394 @default.
- W2055165045 cites W2041263603 @default.
- W2055165045 cites W2044718432 @default.
- W2055165045 cites W2046291899 @default.
- W2055165045 cites W2048313634 @default.
- W2055165045 cites W2048610309 @default.
- W2055165045 cites W2050920629 @default.
- W2055165045 cites W205172853 @default.
- W2055165045 cites W2063339487 @default.
- W2055165045 cites W2064433981 @default.
- W2055165045 cites W2070217890 @default.
- W2055165045 cites W2073052087 @default.
- W2055165045 cites W2075190498 @default.
- W2055165045 cites W2076536265 @default.
- W2055165045 cites W2077114464 @default.
- W2055165045 cites W2077601888 @default.
- W2055165045 cites W2077799553 @default.
- W2055165045 cites W2078460128 @default.
- W2055165045 cites W2079937222 @default.
- W2055165045 cites W2080638865 @default.
- W2055165045 cites W2083828328 @default.
- W2055165045 cites W2089592010 @default.
- W2055165045 cites W2090402431 @default.
- W2055165045 cites W2097116423 @default.
- W2055165045 cites W2115998098 @default.
- W2055165045 cites W2133240766 @default.
- W2055165045 cites W2158303775 @default.
- W2055165045 cites W2168246597 @default.
- W2055165045 cites W2227304090 @default.
- W2055165045 cites W2242726335 @default.
- W2055165045 cites W2262184227 @default.
- W2055165045 cites W2281727696 @default.
- W2055165045 cites W2298484929 @default.
- W2055165045 cites W2312285547 @default.
- W2055165045 cites W2316991291 @default.
- W2055165045 cites W2317261924 @default.
- W2055165045 cites W2317876074 @default.
- W2055165045 cites W2317977625 @default.
- W2055165045 cites W2318358641 @default.
- W2055165045 cites W2318411205 @default.
- W2055165045 cites W2318648068 @default.
- W2055165045 cites W2319033251 @default.
- W2055165045 cites W2319134735 @default.
- W2055165045 cites W2320266418 @default.
- W2055165045 cites W2321957512 @default.
- W2055165045 cites W2323328428 @default.