scholarly journals LEBESGUE INTEGRABILITY IMPLIES GENERALIZED RIEMANN INTEGRABILITY IN ℝ ]0, 1]

2001 ◽  
Vol 27 (1) ◽  
pp. 223 ◽  
Author(s):  
Muldowney ◽  
Skvortsov
Keyword(s):  
Lebesgue Integrability

LEBESGUE INTEGRABILITY OF DOUBLE COSINE AND SINE SERIES

Analysis ◽  
1993 ◽  
Vol 13 (4) ◽  
pp. 321-350
Author(s):  
Ferenc Móricz
Keyword(s):  
Sine Series ◽  
Lebesgue Integrability

scholarly journals Properties of the Riemann–Lebesgue integrability in the non-additive case

2019 ◽  
Vol 69 (2) ◽  
pp. 577-589 ◽  
Author(s):  
Domenico Candeloro ◽  
Anca Croitoru ◽  
Alina Gavriluţ ◽  
Alina Iosif ◽  
Anna Rita Sambucini
Keyword(s):  
Lebesgue Integrability

scholarly journals Statistical Riemann and Lebesgue Integrable Sequence of Functions with Korovkin-Type Approximation Theorems

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 229
Author(s):  
Hari Mohan Srivastava ◽  
Bidu Bhusan Jena ◽  
Susanta Kumar Paikray
Keyword(s):  
Limit Theorems ◽  
Bernstein Polynomials ◽  
Linear Operators ◽  
Test Functions ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Korovkin Type Approximation Theorems ◽  
Algebraic Test ◽  
Lebesgue Summability ◽  
Lebesgue Integrability

In this work we introduce and investigate the ideas of statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful and potentially useful notions. Furthermore, based upon our proposed techniques, we establish the Korovkin-type approximation theorems with algebraic test functions. Finally, we present two illustrative examples under the consideration of positive linear operators in association with the Bernstein polynomials to exhibit the effectiveness of our findings.

Perron Integrability Versus Lebesgue Integrability

1985 ◽  
Vol 28 (4) ◽  
pp. 463-468 ◽  
Author(s):  
Arlo W. Schurle
Keyword(s):  
Integrable Function ◽  
Measure Theory ◽  
The Relationship ◽  
Dense Set ◽  
Lebesgue Integrability

AbstractThe paper investigates the relationship between Perron - Stieltjes integrability and Lebesgue-Stieltjes integrability within the generalized Riemann approach. The main result states that with certain restrictions a Perron-Stieltjes integrable function is locally Lebesgue-Stieltjes integrable on an open dense set. This is then applied to show that a nonnegative Perron-Stieltjes integrable function is Lebesgue-Stieltjes integrable. Finally, measure theory is invoked to remove the restrictions in the main result.

Riemann and Lebesgue Integrability

1972 ◽  
Vol s2-5 (3) ◽  
pp. 459-464 ◽  
Author(s):  
Samuel Kaplan
Keyword(s):  
Lebesgue Integrability

scholarly journals The Riemann-Lebesgue Integral of Interval-Valued Multifunctions

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2250
Author(s):  
Danilo Costarelli ◽  
Anca Croitoru ◽  
Alina Gavriluţ ◽  
Alina Iosif ◽  
Anna Rita Sambucini
Keyword(s):  
Image Coding ◽  
Detection Algorithm ◽  
Visual Signal ◽  
Lebesgue Integral ◽  
Order Continuity ◽  
Fractal Image ◽  
Fractal Image Coding ◽  
Interval Valued ◽  
Discretization Process ◽  
Lebesgue Integrability

We study Riemann-Lebesgue integrability for interval-valued multifunctions relative to an interval-valued set multifunction. Some classic properties of the RL integral, such as monotonicity, order continuity, bounded variation, convergence are obtained. An application of interval-valued multifunctions to image processing is given for the purpose of illustration; an example is given in case of fractal image coding for image compression, and for edge detection algorithm. In these contexts, the image modelization as an interval valued multifunction is crucial since allows to take into account the presence of quantization errors (such as the so-called round-off error) in the discretization process of a real world analogue visual signal into a digital discrete one.

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