Linear Operators: General theory |
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Page 195
Indeed , according to Tonelli ' s theorem , both these integrals are equal to the
integral off with respect to the product measure ( and we have already remarked
that the product of measures is commutative . ) Generalizing this statement , and
...
Indeed , according to Tonelli ' s theorem , both these integrals are equal to the
integral off with respect to the product measure ( and we have already remarked
that the product of measures is commutative . ) Generalizing this statement , and
...
Page 227
Lett be analytic in V - A . Then the second form of Cauchy ' s integral theorem
states : If we agree to orient the Jordan ... and is independent of any particular
choice of the neighborhood U of A . In other words , the integrals SB and SB , are
...
Lett be analytic in V - A . Then the second form of Cauchy ' s integral theorem
states : If we agree to orient the Jordan ... and is independent of any particular
choice of the neighborhood U of A . In other words , the integrals SB and SB , are
...
Page 232
The possibility of extending the integral to this realm was recognized by L . M .
Graves [ 3 ] , who discussed and applied the Riemann integral . A theory of the
Lebesgue type was constructed by Bochner [ 2 ] . The Cauchy sequence method
of ...
The possibility of extending the integral to this realm was recognized by L . M .
Graves [ 3 ] , who discussed and applied the Riemann integral . A theory of the
Lebesgue type was constructed by Bochner [ 2 ] . The Cauchy sequence method
of ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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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