Daguerreotype 发表于 2025-3-21 18:32:40
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Basic Integrals, with the integration of the simplest functions on such a space. A full-fledged measure space and the integration of a quite general type of function on such a space will then be derived by a natural species of approximation, in Chap. 3.adhesive 发表于 2025-3-22 03:15:04
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Convergence and Differentiation,o obtain a similarly penetrating theory when the vector space is infinite-dimensional without additional structure in the space. A first step in civilizing a linear space for the purposes of analysis is the introduction of a convenient topology, i.e. one with respect to which relevant operations arebrachial-plexus 发表于 2025-3-22 11:08:17
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Function Spaces,eral theory. The primary result in the finite-dimensional case is that the natural injection of . into the dual .** of . is an isomorphism of . onto .**. This means that if . is an element of . and . denotes the element of .** given by the equation .**(.) = .(.) for all . in .*, then the map . → .**insipid 发表于 2025-3-22 19:18:22
Invariant Integrals,nd interact with the integration features, so that the additional features cannot really be considered separately. The simplest and most common such additional feature is a topology on the set under consideration, on which the measure in question is defined. Some indications have already been givenFlirtatious 发表于 2025-3-23 00:00:56
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Group Representations and Unbounded Operators,heory to unbounded operators, and related developments in group-representation theory. The theorem of Stone, giving the structure of the general one-parameter continuous unitary group on a Hilbert space, connects with both these matters and is intrinsically important. Its analogs for groups which ar