Improper Riemann Integral and Henstock Integral in ℝn

P. Muldowney; V. A. Skvortsov

doi:10.1007/s11006-005-0119-7

Improper Riemann Integral and Henstock Integral in ℝn

Mathematical Notes ◽

10.1007/s11006-005-0119-7 ◽

2005 ◽

Vol 78 (1-2) ◽

pp. 228-233 ◽

Cited By ~ 1

Author(s):

P. Muldowney ◽

V. A. Skvortsov

Keyword(s):

Henstock Integral ◽

Riemann Integral

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SIFAT-SIFAT DASAR INTEGRAL HENSTOCK

BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN ◽

10.30598/barekengvol6iss2pp7-15 ◽

2012 ◽

Vol 6 (2) ◽

pp. 7-15

Author(s):

Lexy J. Sinay

Keyword(s):

Positive Constant ◽

Positive Function ◽

Henstock Integral ◽

Riemann Integral ◽

Basic Properties ◽

Definition Of ◽

Integration Area

This paper was a review about theory of Henstock integral. Riemann gave a definition of integral based on the sum of the partitions in Integration area (interval [a, b]). Thosepartitions is a  -positive constant. Independently, Henstock and Kurzweil replaces - positive constant on construction Riemann integral into a positive function, ie (x)>0 forevery x[a, b]. This function is a partition in interval [a, b]. From this partitions, we can defined a new integral called Henstock integral. Henstock integral is referred to as acomplete Riemann integral, because the basic properties of the Henstock integral is more constructive than Riemann Integral.

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Fundamental theorem of calculus under weaker forms of primitive

Acta Universitatis Sapientiae Mathematica ◽

10.2478/ausm-2018-0009 ◽

2018 ◽

Vol 10 (1) ◽

pp. 101-111

Author(s):

Nisar A. Lone ◽

T. A. Chishti

Keyword(s):

Convex Space ◽

Fundamental Theorem ◽

Locally Convex Space ◽

Henstock Integral ◽

Riemann Integral ◽

Infinite Dimensional ◽

Fundamental Theorem Of Calculus ◽

Locally Convex

Abstract In this paper we will present abstract versions of fundamental theorem of calculus (FTC) in the setting of Kurzweil - Henstock integral for functions taking values in an infinite dimensional locally convex space. The result will also be dealt with weaker forms of primitives in a widespread setting of integration theories generalising Riemann integral.

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Hubungan antara Integral Henstock dengan Integral Henstockdelta pada Skala Waktu

JMT : Jurnal Matematika dan Terapan ◽

10.21009/jmt.1.1.2 ◽

2017 ◽

Vol 1 (1) ◽

pp. 10-14

Author(s):

Albert Parulian ◽

Sudarwanto Sudarwanto ◽

Ibnu Hadi

Keyword(s):

Henstock Integral ◽

Riemann Integral

Abstrak Penelitian ini membahas bagaimana hubungan antara Integral Henstock dengan Integral Henstock-Delta pada skala waktu. Konsep dasar dari kedua integral tersebut terletak pada pembentukan partisi yang muncul pada konsep Integral Riemann. Perluasan konsep ini yang menjadi dasar dalam hubungan antara Integral Henstock dengan Integral Henstock-Delta pada skala waktu. Hubungan tersebut tertuang dalam teorema, misalkan terdefinisikan pada skala waktu dan didefinisikan oleh sehingga jika terintegralkan Henstock pada selang maka terintegralkan Henstock-Delta pada skala waktu. Kata kunci : Integral Riemann, Integral Henstock, Integral Henstock-Delta, skala waktu, partisi .

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