Authors: and
View More View Less
• 1 University of Szeged Bolyai Institute Aradi vértanúk tere 1 H-6720 Szeged Hungary
• 2 Universität Ulm Abt. Zahlentheorie und Wahrscheinlichkeitstheorie D-89069 Ulm Germany
Restricted access

USD  $25.00 ### 1 year subscription (Individual Only) USD$800.00

Let ν be a positive Borel measure on ℝ̄+:= [0;∞) and let p: ℝ̄+ → ℝ̄+ be a weight function which is locally integrable with respect to ν. We assume that \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $P(t): = \int\limits_0^t {p(u)d\nu (u) \to \infty } andP(t - 0)/P(t) \to 1ast \to \infty .$ \end{document} Let f: ℝ̄+ → ℂ be a locally integrable function with respect to p dν, and define its weighted averages by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\sigma _t (f;pd\nu ): = \frac{1}{{P(t)}}\int\limits_0^t {f(u)p(u)d\nu (u)}$ \end{document} for large enough t, where P(t) > 0. We prove necessary and sufficient conditions under which the finite limit \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\sigma _t (f;pd\nu ) \to Last \to \infty$ \end{document} exists. This characterization is a unified extension of the results in [5], and it may find application in Probability Theory and Stochastic Processes.

• Agnew, R. P., On deferred Cesàro means, Annals of Math. (2), 33 (1932), 413–421.

Agnew R. P. , 'On deferred Cesàro means ' (1932 ) 33 Annals of Math. (2) : 413 -421.

• Berkes, I., Csáki, E. and Horváth, L., An almost sure central limit theorem under minimal conditions, Stat Probab. Letters, 37 (1998), 67–76.

Horváth L. , 'An almost sure central limit theorem under minimal conditions ' (1998 ) 37 Stat Probab. Letters : 67 -76.

• Hardy, G. H., Divergent Series, Clarendon Press, Oxford, 1949.

Hardy G. H. , '', in Divergent Series , (1949 ) -.

• Móricz, F., On the harmonic averages of numerical sequences, Arch. Math. (Basel), 86 (2006), 375–384.

Móricz F. , 'On the harmonic averages of numerical sequences ' (2006 ) 86 Arch. Math. (Basel) : 375 -384.

• Móricz, F. and Stadtmüller, U., Characterization of the convergence of weighted averages of sequences and functions, Periodica Math. Hungar., 65 (2012), 135–145.

Stadtmüller U. , 'Characterization of the convergence of weighted averages of sequences and functions ' (2012 ) 65 Periodica Math. Hungar. : 135 -145.

• Révész, P., The Laws of Large Numbers, Akadémiai Kiadó, Budapest, 1967.

Révész P. , '', in The Laws of Large Numbers , (1967 ) -.

• Witting, H., Mathematische Statistik, Vol. I, B. G. Teubner Verlag, Stuttgart, 1985.

Witting H. , '', in Mathematische Statistik , (1985 ) -.

• Zygmund, A., Trigonometric Series, Vol. I, Cambridge Univ. Press, 1959.

May 2020 0 6 3
Jun 2020 0 0 0
Jul 2020 1 0 0
Aug 2020 1 0 0
Sep 2020 0 0 0
Oct 2020 0 0 0
Nov 2020 0 0 0

## On Weakly-neighbourly polyhedra

Author: A. Bölcseki

## On the distribition of residue classes of quadratic forms and integer-detecting sequences in number fields

Authors: C. Elsner and J. W. Sander

## Chogomogeneity one G-pseudomanifolds

Author: R. Popper

## A right inverse function theorem withhout assuming differentiability

Author: B. Slezák

## Lower classes of integrated fractional Brownian motion

Author: C. El-Nouty