On the Marcinkiewicz theorem for the binary Perron integral

1996 ◽  
Vol 59 (2) ◽  
pp. 189-195
Author(s):  
V. A. Skvortsov
Keyword(s):  
Marcinkiewicz Theorem ◽  
Perron Integral

scholarly journals A wide Perron integral

1986 ◽  
Vol 34 (2) ◽  
pp. 233-251
Author(s):  
D. N. Sarkhel
Keyword(s):  
Decomposition Theorem ◽  
Mean Value ◽  
Lebesgue Decomposition ◽  
Integration By Parts ◽  
Mean Value Theorems ◽  
Limit Process ◽  
Real Functions ◽  
Marcinkiewicz Theorem ◽  
Perron Integral ◽  
Interesting Generalization

In terms of an arbitrary limit process T, defined abstractly for real functions, we define in a novel way a T-continuous integral of Perron type, admitting mean value theorems, integration by parts and the analogue of the Marcinkiewicz theorem for the ordinary Perron integral. The integral is shown to include, as particular cases, the various known continuous, approximately continuous, cesàro-continuous, mean-continuous and proximally Cesàro-continuous integrals of Perron and Denjoy types. An interesting generalization of the classical Lebesgue decomposition theorem is also obtained.

scholarly journals (PVB) functions and integration

1984 ◽  
Vol 36 (3) ◽  
pp. 335-353 ◽  
Author(s):  
D. N. Sarkhel ◽  
A. B. Kar
Keyword(s):  
Real Line ◽  
Mean Value ◽  
Integration By Parts ◽  
The Real ◽  
Mean Value Theorems ◽  
Marcinkiewicz Theorem ◽  
Perron Integral

AbstractWe introduce the notion of functions of bounded proximal variation and the notion of orderly connected topology on the real line. Using these notions, we define in a novel way an integral of Perron type, including virtually all the known integrals of Perron and Denjoy types and admitting mean value theorems and integration by parts and the analog of Marcinkiewicz theorem for the ordinary Perron integral.

INTEGRATION BY PARTS FOR THE PERRON INTEGRAL

1990 ◽  
Vol 16 (2) ◽  
pp. 546
Author(s):  
Cross
Keyword(s):  
Integration By Parts ◽  
Perron Integral

The Representation of (C, k) Summable Series in Fourier Form

1978 ◽  
Vol 21 (2) ◽  
pp. 149-158 ◽  
Author(s):  
G. E. Cross
Keyword(s):  
Trigonometric Series ◽  
Point Of View ◽  
Perron Integral ◽  
Image Position

Several non-absolutely convergent integrals have been defined which generalize the Perron integral. The most significant of these integrals from the point of view of application to trigonometric series are the Pn- and pn-integrals of R. D. James [10] and [11]. The theorems relating the Pn -integral to trigonometric series state essentially that if the series1.1

scholarly journals THE STRONG PERRON INTEGRAL

2003 ◽  
Vol 40 (1) ◽  
pp. 77-83
Author(s):  
Byung-Moo Kim ◽  
Young-Kuk Kim ◽  
Jae-Myung Park
Keyword(s):  
Perron Integral

The Perron Integral

1994 ◽  
pp. 121-136
Author(s):  
Russell Gordon
Keyword(s):  
Perron Integral

The Controlled Convergence Theorem for the Gap-Integral

2015 ◽  
Vol 65 (5) ◽  
Author(s):  
D. K. Ganguly ◽  
Ranu Mukherjee
Keyword(s):  
Convergence Theorem ◽  
Convergence Theorems ◽  
Perron Integral

AbstractThe concept of the GAP-integral was introduced by the authors [GANGULY, D. K.-MUKHERJEE, R.: The generalized approximate Perron integral, Math. Slovaca 58 (2008), 31-42]. In this paper we prove the controlled convergence theorem for the GAP-integral and deduce other convergence theorems as corollaries.

Stability for the Marcinkiewicz theorem. Case of a fourth-degree polynomial

1981 ◽  
Vol 16 (5) ◽  
pp. 1413-1424
Author(s):  
N. A. Sapogov
Keyword(s):  
Degree Polynomial ◽  
Fourth Degree ◽  
Marcinkiewicz Theorem

scholarly journals The Cauchy property of the generalized approximately continuous Perron integral

1960 ◽  
Vol 12 (2) ◽  
pp. 171-174 ◽  
Author(s):  
Yôto Kubota
Keyword(s):  
Perron Integral
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