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Page 6
... which proves the assertion ( v ) . It will next be shown that P is admissible . The
condition ( i ) is vacuously satisfied by P . To prove that P has the property ( ii ) ,
let X e P . It will be shown that if z € A , and 2 < f ( x ) , then f ( x ) = f ( x ) . From ( v )
...
... which proves the assertion ( v ) . It will next be shown that P is admissible . The
condition ( i ) is vacuously satisfied by P . To prove that P has the property ( ii ) ,
let X e P . It will be shown that if z € A , and 2 < f ( x ) , then f ( x ) = f ( x ) . From ( v )
...
Page 156
... are explicitly discussed in the next chapter , where it is shown that the
conjugate spaces of some familiar B - spaces may be represented in terms of set
functions . In the present section it will be shown that the spaces of bounded
additive set ...
... are explicitly discussed in the next chapter , where it is shown that the
conjugate spaces of some familiar B - spaces may be represented in terms of set
functions . In the present section it will be shown that the spaces of bounded
additive set ...
Page 335
It will first be shown that W satisfies the hypothesis of Zorn ' s lemma . To do this
we let W , be a totally ordered subset of W ( 1 . 22 ) and let c CUW . . Then , for
some a e W . , cna is not void . Let æ be the smallest element of cna and let y be ...
It will first be shown that W satisfies the hypothesis of Zorn ' s lemma . To do this
we let W , be a totally ordered subset of W ( 1 . 22 ) and let c CUW . . Then , for
some a e W . , cna is not void . Let æ be the smallest element of cna and let y be ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
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algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero