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Page 240
The space bs is the linear space of all sequences x = { an } of scalars for which the norm n | x = sup ail n i = 1 n is ... E ) is given by the formula sup \ | ( 8 ) SES A scalar function f on S is E - measurable if f ( A ) € for every ...
The space bs is the linear space of all sequences x = { an } of scalars for which the norm n | x = sup ail n i = 1 n is ... E ) is given by the formula sup \ | ( 8 ) SES A scalar function f on S is E - measurable if f ( A ) € for every ...
Page 256
If , however , each of the spaces X1 , ... , Xn are Hilbert spaces then it will always be understood , sometimes without explicit mention , that X is the uniquely determined Hilbert space with scalar product n ( iv ) ( [ x , ... , Xn ] ...
If , however , each of the spaces X1 , ... , Xn are Hilbert spaces then it will always be understood , sometimes without explicit mention , that X is the uniquely determined Hilbert space with scalar product n ( iv ) ( [ x , ... , Xn ] ...
Page 323
A scalar valued measurable function f is said to be integrable if there exists a sequence { { n } of simple functions such that ( i ) fn ( s ) converges to f ( s ) u - almost everywhere ; ( ii ) the sequence { Sein ( s ) ...
A scalar valued measurable function f is said to be integrable if there exists a sequence { { n } of simple functions such that ( i ) fn ( s ) converges to f ( s ) u - almost everywhere ; ( ii ) the sequence { Sein ( s ) ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero