Arzela's Dominated Convergence Theorem for the Riemann Integral

1971 ◽  
Vol 78 (9) ◽  
pp. 970 ◽  
Author(s):  
W. A. J. Luxemburg
Keyword(s):  
Convergence Theorem ◽  
Riemann Integral ◽  
Dominated Convergence

scholarly journals A dominated convergence theorem for Eisenstein series

2021 ◽  
Author(s):  
Johann Franke
Keyword(s):  
Fourier Series ◽  
Dirichlet Series ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Convergence Theorem ◽  
Rational Functions ◽  
New Approach ◽  
Series Representations ◽  
Dominated Convergence ◽  
Generalized Dirichlet

AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.

scholarly journals On Fuzzy Henstock-Kurzweil-Stieltjes-♦-Double Integral on Time scales

2021 ◽  
Vol 2 (2) ◽  
pp. 38-49
Author(s):  
David AFARIOGUN ◽  
Adesanmi MOGBADEMU ◽  
Hallowed OLAOLUWA
Keyword(s):  
Uniform Convergence ◽  
Time Scales ◽  
Convergence Theorem ◽  
Monotone Convergence ◽  
Double Integral ◽  
Monotone Convergence Theorem ◽  
Integrable Functions ◽  
Dominated Convergence

We introduce and study some properties of fuzzy Henstock-Kurzweil-Stietljes-$ \Diamond $-double integral on time scales. Also, we state and prove the uniform convergence theorem, monotone convergence theorem and dominated convergence theorem for the fuzzy Henstock-Kurzweil Stieltjes-$\Diamond$-double integrable functions on time scales.

A Convergence Theorem for the Riemann Integral

2000 ◽  
Vol 73 (2) ◽  
pp. 141-147
Author(s):  
Russell A. Gordon
Keyword(s):  
Convergence Theorem ◽  
Riemann Integral

scholarly journals A DOMINATED CONVERGENCE THEOREM IN THE K-H INTEGRAL

2003 ◽  
Vol 7 (3) ◽  
pp. 507-512
Author(s):  
Jitan Lu ◽  
Peng-Yee Lee
Keyword(s):  
Convergence Theorem ◽  
Dominated Convergence
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