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77 sonuçtan 1-3 arası sonuçlar
Sayfa 754
Finally , returning to the initial scale ( N states ) , we obtain the desired estimate .
O Now we present a corollary concerning a uniform law of large numbers .
Corollary . Let Fe , h be the class of functions on the state space of a Bernoulli
scheme ...
Finally , returning to the initial scale ( N states ) , we obtain the desired estimate .
O Now we present a corollary concerning a uniform law of large numbers .
Corollary . Let Fe , h be the class of functions on the state space of a Bernoulli
scheme ...
Sayfa 831
Iterating this estimate , after m steps we conclude that w ( z ) < { ( h + 8 ) ( 1 – ( 1-8
) " ) + as1 -8 ) " } y for all z = ( x , y ) e Rņ + 1 If m is sufficiently large , then the right
- hand side of this inequality is less than ( h + 2 € ) y . Since & > 0 is arbitrary ...
Iterating this estimate , after m steps we conclude that w ( z ) < { ( h + 8 ) ( 1 – ( 1-8
) " ) + as1 -8 ) " } y for all z = ( x , y ) e Rņ + 1 If m is sufficiently large , then the right
- hand side of this inequality is less than ( h + 2 € ) y . Since & > 0 is arbitrary ...
Sayfa 1140
Now the first estimate in ( 3.2 ) follows from ( 3.16 ) , and the third one from ( 3.10
) . In order to establish the second estimate in ( 3.2 ) , we apply Theorem 3 from [
18 ] to the function v . Using ( 3.12 ) , ( 3.13 ) , ( 3.11 ) , and the third estimate in ...
Now the first estimate in ( 3.2 ) follows from ( 3.16 ) , and the third one from ( 3.10
) . In order to establish the second estimate in ( 3.2 ) , we apply Theorem 3 from [
18 ] to the function v . Using ( 3.12 ) , ( 3.13 ) , ( 3.11 ) , and the third estimate in ...
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İçindekiler
THE THEORY OF DECREASING SEQUENCES | 706 |
1 Main definitions and terminology | 712 |
Theorem on lacunary isomorphism | 719 |
Telif Hakkı | |
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Diğer baskılar - Tümünü görüntüle
Sık kullanılan terimler ve kelime öbekleri
action algebra analytic apply approximation arbitrary assume belongs boundary bounded called closed coefficients coincides compact complete condition cone Consequently consider consists constant constructed contains continuous Corollary corresponding defined definition denote depends determined differential domain elements English transl equal equation equivalent estimate example exists finite fixed follows formula function given homogeneous ideal identity implies independent inequality integral introduce invariant irreducible isomorphic Lemma limit linear mapping Math Mathematical means measure metric Moreover neighborhood obtain operator parabolic particular partition plane polynomials positive problem projection Proof properties Proposition proved relation Remark representation respect satisfying sequence similar smooth solution space spectrum standard statement Subsection sufficiently Theorem theory transformation valid values variables vector weight zero