Illinois Journal of Mathematics, Volume 7University of Illinois Press, 1963 - Electronic journals |
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Page 60
for every summable ƒ , and it is the purpose of this paper to prove this con- jecture . In fact , we prove a little more than this . We take the subclass K of C , consisting of all Lipschitz functions , let K1 be the completion of K ...
for every summable ƒ , and it is the purpose of this paper to prove this con- jecture . In fact , we prove a little more than this . We take the subclass K of C , consisting of all Lipschitz functions , let K1 be the completion of K ...
Page 285
... prove that u Ui + 1 , and for this it is sufficient to prove that Um Cut for all mi + 1 . For sufficiently large m , we have Umu . Suppose for some m≥ i + 1 , we have Um + j ≤ U111 for j 1 , 2 , ... . In order to prove that Um Cui1 ...
... prove that u Ui + 1 , and for this it is sufficient to prove that Um Cut for all mi + 1 . For sufficiently large m , we have Umu . Suppose for some m≥ i + 1 , we have Um + j ≤ U111 for j 1 , 2 , ... . In order to prove that Um Cui1 ...
Page 297
... prove ( i ) Proof . ( i ) We may assume that [ E - a Ea ; ] Let mo Ea ; 0 for 0 ≤ v≤ k − 1 , and m 。 E .; it is sufficient to prove that k = p , because of the well known classification of the irreducible restricted modules for the ...
... prove ( i ) Proof . ( i ) We may assume that [ E - a Ea ; ] Let mo Ea ; 0 for 0 ≤ v≤ k − 1 , and m 。 E .; it is sufficient to prove that k = p , because of the well known classification of the irreducible restricted modules for the ...
Contents
FUCHS W H J Proof of a conjecture of G Pólya concerning | 8 |
GRANIRER E On amenable semigroups with a finitedimensional | 58 |
Hu SZETSEN Immersions of compact metric spaces into Euclidean | 80 |
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2-group a₁ abelian algebra assume B₁ Banach Banach algebra Borel Borel set bounded Brownian motion cochain commutative compact completes the proof condition contains converges COROLLARY countable decomposition defined definition denote dense element epimorphism equivalent exists f-algebra finite groups follows function g₁ H₁ h₂ hence homomorphism homotopy idempotent idempotent factors identity implies indecomposable induced infinitely divisible infinitely divisible distribution integer IP-algebra irreducible isoclinic isometries isomorphic l-prime L₁ left amenable left ideal Lemma linear martingale Math matrix maximal measure MI(G module nonnegative nonzero norm O-subdivision orthogonal P₁ P₂ polynomials projective proof of Theorem Proposition prove R-module real numbers representation result right ideal ring sample paths satisfies Section semigroup sequence space subgroup subset subspace Suppose t₁ Theorem Theorem 2.1 topology totally geodesic V₁ vector X₁ y₁ zero