Results 241 to 250 of about 1,296,348 (280)

Convergence of Certain Probability Distribution Functions

Mathematische Nachrichten, 1980
AbstractProperties of the space of one‐dimensional continuous probability distribution functions endowed with the topology of pointwise convergence are investigated. For example, the operation of convolution is shown to be continuous.
McKennon, Kelly, Richardson, Gary
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Convergent Extensions of Grid‐Functions

Mathematische Nachrichten, 1988
AbstractIt is well‐known that functions u ϵ Wm,p (Ω) can be extended by a bounded linear operator E to functions Eu ≦ Wm,p(Rn), if Ω is CM‐regular and m ≦ M. Here we prove a corresponding result for grid‐functions with extension operators Eh converging to E and mention some applications.
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Weak Convergence of a Certain Functional

Theory of Probability & Its Applications, 2002
Summary: We consider the functional \(T_n=(S_1^2+\cdots+S_n^2)/(nV_n^2)\) derived from a sequence \(\{X_n\}_{n\geq 1}\) of independent identically distributed random variables, where \(S_k=X_1+\cdots+X_k\), \(V_n^2=X_1^2+\cdots+X_n^2\). Let \(G\) be the distribution function of the random variable \(\int_{0}^{1}W^2(t) dt\), where \(W(t)\), \(t\in [0,1]\
Kruglov, V. M., Petrovskaya, G. N.
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CONVERGENCE OF CERTAIN FUNCTIONAL SERIES

Mathematics of the USSR-Izvestiya, 1967
Using the idea of extension of the system of functions {fk(x)} to an orthogonal one, the author establishes some assertions relating to convergence, (C,1)-summability and unconditional convergence almost everywhere of series in the system {fk(x)}.
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Convergence of Functions

2011
In many situations we have a sequence of functions f n that converges to some function f and f is not easy to study directly. Can we use the functions f n to get some information about f? For instance, if the f n are continuous, is f necessarily continuous?
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Convergence of Functions

2015
Major convergence concepts for sequences of real-valued functions will be considered in this chapter. We have already met four convergence concepts so far (viz., pointwise, uniform, almost everywhere, and convergence in L p ). These are reviewed and compared in this section.
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Strong convergence of additive arithmetic functions

Lithuanian Mathematical Journal, 1985
Given an additive function f let \(f_ k\) (k\(\geq 1)\) be the associated ''truncated'' functions defined by \(f_ k(n)=\sum_{p^ m\| n, p\leq k}f(p^ m).\) The author first characterizes those additive functions f, for which the sequence \((f_ k)\) converges strongly to f in the sense that for every \(\epsilon >0\) \[ \lim_{k\to \infty} \limsup_{x\to ...
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Convergence of Subdifferentials of Convexly Composite Functions

Canadian Journal of Mathematics, 1999
AbstractIn this paper we establish conditions that guarantee, in the setting of a general Banach space, the Painlevé-Kuratowski convergence of the graphs of the subdifferentials of convexly composite functions. We also provide applications to the convergence of multipliers of families of constrained optimization problems and to the generalized second ...
Combari, C., Poliquin, R., Thibault, L.
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CONVERGENCE OF INTEGRAL FUNCTIONALS OF STOCHASTIC PROCESSES

Econometric Theory, 2006
Summary: We investigate the convergence in distribution of integrals of stochastic processes satisfying a functional limit theorem. We allow a large class of continuous Gaussian processes in the limit. Depending on the continuity properties of the underlying process, local Lebesgue or Riemann integrability is required.
Berkes, István, Horváth, Lajos
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On Uniform Convergence of Continuous Functions and Topological Convergence of Sets

Canadian Mathematical Bulletin, 1983
AbstractLet X and Y be metric spaces. This paper considers the relationship between uniform convergence in C(X, Y) and topological convergence of functions in C(X, Y), viewed as subsets of X×Y. In general, uniform convergence in C(X, Y) implies Hausdorff metric convergence which, in turn, implies topological convergence, but if X and Y are compact ...
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