Pointwise convergence almost everywhere

2015 ◽  
pp. 19-172
Keyword(s):  
Pointwise Convergence ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere

THE PRINCIPLE OF CONVERGENCE "ALMOST EVERYWHERE" IN LIE GROUPS

1973 ◽  
Vol 20 (4) ◽  
pp. 543-555
Author(s):  
V M Maksimov
Keyword(s):  
Lie Groups ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere

scholarly journals POINTWISE CONVERGENCE AND SEMIGROUPS ACTING ON VECTOR-VALUED FUNCTIONS

2011 ◽  
Vol 84 (1) ◽  
pp. 44-48 ◽  
Author(s):  
MICHAEL G. COWLING ◽  
MICHAEL LEINERT
Keyword(s):  
Banach Space ◽  
Pointwise Convergence ◽  
Function Spaces ◽  
Semigroup Of Operators ◽  
Almost Everywhere ◽  
Vector Valued Function ◽  
Vector Valued Functions ◽  
Complex Valued ◽  
Vector Valued

AbstractA submarkovian C0 semigroup (Tt)t∈ℝ+ acting on the scale of complex-valued functions Lp(X,ℂ) extends to a semigroup of operators on the scale of vector-valued function spaces Lp(X,E), when E is a Banach space. It is known that, if f∈Lp(X,ℂ), where 1<p<∞, then Ttf→f pointwise almost everywhere. We show that the same holds when f∈Lp(X,E) .

Convergence Almost Everywhere of Orthorecursive Expansions in Systems of Translates and Dilates

2018 ◽  
pp. 3-11
Author(s):  
Vladimir V. Galatenko ◽  
Taras P. Lukashenko ◽  
Victor A. Sadovnichiy
Keyword(s):  
Convergence Almost Everywhere ◽  
Almost Everywhere

scholarly journals Strong Law of Large Numbers of the Offspring Empirical Measure for Markov Chains Indexed by Homogeneous Tree

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Huilin Huang
Keyword(s):  
Markov Chains ◽  
Law Of Large Numbers ◽  
Empirical Measure ◽  
Homogeneous Tree ◽  
Almost Everywhere Convergence ◽  
Strong Law ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere ◽  
Large Numbers

We study the limit law of the offspring empirical measure and for Markov chains indexed by homogeneous tree with almost everywhere convergence. Then we prove a Shannon-McMillan theorem with the convergence almost everywhere.

Some Pointwise Convergence Results in Lp(μ), 1 < p < ∞

1977 ◽  
Vol 20 (3) ◽  
pp. 277-284 ◽  
Author(s):  
Richard Duncan
Keyword(s):  
Probability Theory ◽  
Pointwise Convergence ◽  
Function Spaces ◽  
Almost Everywhere Convergence ◽  
Measurable Functions ◽  
Almost Everywhere ◽  
Convergence Results ◽  
Convergence In Norm

The theory of almost everywhere convergence has its roots in the poineering work of A. Kolmogorov, and today it constitutes one of the most captivating and challenging chapters in modern probability theory and analysis. Whereas some modes of convergence for sequences of measurable functions, e.g. convergence in norm, can be readily obtained by an intelligent exploitation of the various properties of the function spaces involved, a.e. convergence invariably requires a rather high, and sometimes surprising, degree of mathematical virtuosity.

scholarly journals CONVERGENCE ALMOST EVERYWHERE OF OPERATOR AVERAGES

1955 ◽  
Vol 41 (4) ◽  
pp. 229-231 ◽  
Author(s):  
N. Dunford ◽  
J. Schwartz
Keyword(s):  
Convergence Almost Everywhere ◽  
Almost Everywhere

scholarly journals On the convergence almost everywhere of double Fourier series

1976 ◽  
Vol 14 (1-2) ◽  
pp. 1-8 ◽  
Author(s):  
Per Sjölin
Keyword(s):  
Fourier Series ◽  
Double Fourier Series ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere

A Martingale Convergence Theorem in Vector Lattices

1966 ◽  
Vol 18 ◽  
pp. 424-432 ◽  
Author(s):  
Ralph DeMarr
Keyword(s):  
Convergence Theorem ◽  
Vector Lattice ◽  
Random Variables ◽  
Order Convergence ◽  
Arbitrary Vector ◽  
Martingale Convergence Theorem ◽  
Convergence Almost Everywhere ◽  
Vector Lattices ◽  
Almost Everywhere ◽  
Martingale Convergence

The martingale convergence theorem was first proved by Doob (3) who considered a sequence of real-valued random variables. Since various collections of real-valued random variables can be regarded as vector lattices, it seems of interest to prove the martingale convergence theorem in an arbitrary vector lattice. In doing so we use the concept of order convergence that is related to convergence almost everywhere, the type of convergence used in Doob's theorem.

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