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.

scholarly journals Extended Real-Valued Double Sequence and Its Convergence

2015 ◽  
Vol 23 (3) ◽  
pp. 253-277 ◽  
Author(s):  
Noboru Endou
Keyword(s):  
Convergence Theorem ◽  
Double Sequence ◽  
Monotone Convergence ◽  
Double Sequences ◽  
Monotone Convergence Theorem ◽  
Fatou’S Lemma ◽  
Fatou's Lemma

Abstract In this article we introduce the convergence of extended realvalued double sequences [16], [17]. It is similar to our previous articles [15], [10]. In addition, we also prove Fatou’s lemma and the monotone convergence theorem for double sequences.

scholarly journals A cauchy criterion and a convergence theorem for Riemann-complete integral

1972 ◽  
Vol 13 (1) ◽  
pp. 21-24
Author(s):  
H. W. Pu
Keyword(s):  
Convergence Theorem ◽  
Convergent Sequence ◽  
Monotone Convergence ◽  
Lebesgue Integral ◽  
Necessary And Sufficient Condition ◽  
Integrable Functions ◽  
Type Integral ◽  
Uniformly Convergent ◽  
Necessary And Sufficient ◽  
Generalized Type

In 1957 Kurzweil [1] proved some theorems concerning a generalized type of differential equations by defining a Riemann-type integral, but he did not study its properties beyond the needs of that research. This was done by R. Henstock [2, 3], who named it a Riemann-complete integral. He showed that the Riemann-complete integral includes the Lebesgue integral and that the Levi monotone convergence theorem holds. The purpose of the present paper is to give a necessary and sufficient condition for a function to be Riemann-complete integrable and to establish a termwise integration theorem for a uniformly convergent sequence of Riemann-complete integrable functions.

scholarly journals The Lebesgue Monotone Convergence Theorem

2008 ◽  
Vol 16 (2) ◽  
Author(s):  
Noboru Endou ◽  
Keiko Narita ◽  
Yasunari Shidama
Keyword(s):  
Convergence Theorem ◽  
Monotone Convergence ◽  
Monotone Convergence Theorem

A new proof of the monotone convergence theorem of Lebesgue integral on σ-class

2012 ◽  
Vol 62 (6) ◽  
Author(s):  
Dinh Hoa
Keyword(s):  
Convergence Theorem ◽  
Short Note ◽  
Monotone Convergence ◽  
Lebesgue Integral ◽  
Monotone Convergence Theorem

AbstractIn this short note a new proof of the monotone convergence theorem of Lebesgue integral on σ-class is given.

Integration

2021 ◽  
pp. 80-102
Author(s):  
James Davidson
Keyword(s):  
First Principles ◽  
Convergence Theorem ◽  
Measure Space ◽  
Product Measure ◽  
Monotone Convergence ◽  
General Measure ◽  
Fundamental Properties ◽  
Monotone Convergence Theorem ◽  
Multiple Integrals ◽  
Nikodym Theorem

The concept of an integral on a general measure space is developed from first principles. Riemann–Stieltjes and Lebesgue–Stieltjes integrals are defined. The monotone convergence theorem, fundamental properties of integrals, and related inequalities are covered. Other topics include product measure and multiple integrals, Fubini’s theorem, signed measures, and the Radon–Nikodym theorem.

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