Eine Bemerkung zu einer Arbeit von Heineken und Liebeck

Ohne Zusammenfassung     

A note on a theorem of Yamamuro

Conditions are presented which are necessary for the existence of a regular fixed point of aC ¹ map.Work supported in part by NSF Grant No. MCS 77-15509.Work supported in part by ONR Grant No. N0014-75-C-0495 and NSF Grant No. Eng. 76-81058.     

A note on a theorem of Kanovei

We give a short proof of a theorem of Kanovei on separating induction and collection schemes for _n formulas using families of subsets of countable models of arithmetic coded in elementary end extensions.Mathematics Subject Classification (2000): 03C62     

A note on a theorem of Sunouchi

We show that for negativeα Sunouchi's formula $$\begin{gathered} H_n (f,\alpha ,\beta ,x) = \frac{1}{{A_n^\beta }}\sum\nolimits_{k = 0}^n {A_{n - k}^{\beta - 1} } |f(x) - \sigma _k^\alpha (f,x)|, \hfill \\ \alpha > - \frac{1}{2},\beta > \frac{1}{2}, \hfill \\ \end{gathered}$$ becomes false, where σ _k ^α (f, x) is the (C,α) mean of the Fourier series for the functionf(x) ε Lipγ, 0<γ<1. A bound is given for H_n(f, α,β, x) for allα > -1,β> -1, which forα + β > 0, α≥ 0,β ≥0, coincides with the Sunouchi bound. The proof is by a method different from that of Sunouchi.     

A note on a theorem of Daboussi

The following assertion is proved. Let be the set of integers the number of the prime power of which is . Let be the size of . Then for each irrational , uniformly in , \begin{equation*} \frac{1}{\pi_k(x)} \bigg|\sum _{\alul{n\le x}{n\in\cN_k}} f(n) e^{2\pi in\alpha}\bigg|\to 0, \end{equation*} where is an arbitrary multiplicative function with , is a positive constant. This revised version was published online in June 2006 with corrections to the Cover Date.     

A note on a theorem of Talagrand

We provide an elementary argument to show that if for a hemicompact kR-space X the space Cp(X) contains a subset S which separates the points of X and is dominated by irrationals, i.e. S is covered by a family of compact sets such that Kα⊂Kβ for α?β, then Cp(X) is also dominated by irrationals; consequently Cp(X) is K-analytic. This fact (which fails for non-hemicompact spaces X) extends an old result of Talagrand.     

A note on a theorem of Tacon

In this paper we give the minimal conditions which must satisfy families of subsets ofF for the proof of a theorem of Tacon and analogous results for some other classes of operatorsT:E→F defined via these families can be reproduced.     

A note on a theorem of heath

We propose a generalization of Heath's theorem that semi-metric spaces with point-countable bases are developable: A semi-metrizable space X is developabale if (and only if) there is on it a σ-discrete family $\text{C}\text{=?}{}_{\mathrm{m?N}}\text{C}{}_{\mathrm{m}}$ of closed sets, interior-preserving over each member C of which is a countable family {$\text{D}$_n(C): n ∈ N} of collections of open sets such that if U is a neighbourhood of ξ∈X, then there are such a Γ∈$\text{C}$ and such a v∈ N that ξ ? Γ and ξ∈ int ∩ (D: ξ: D∈$\text{D}$_v(Γ))?U.     

A note on a theorem of Aumann and Dreze

Aumann and Dreze (1974) examine sections of cores of side payments games via cores of reduced games. We study sections of cores of games without side payments.A preliminary version appeared as discussion paper no. 392-89 at the University of Mannheim.     

A note on a theorem of Raubenheimer and Rode

We prove the converse of Raubenheimer and Rode's Banach algebra version of the Perron-Frobenius Theorem.