Henstock-Kurzweilov integral

delo diplomskega seminarja

Miha Jerič (Author), Barbara Drinovec-Drnovšek (Mentor)

Abstract

V diplomskem delu obravnavamo Henstock-Kurzweilov integral. Njegova definicija je podobna Riemannovi, le da finost delitev intervalov določa funkcija $\delta$ in ne več konstanta. Ta razlika omogoči integriranje mnogo splošnejših funkcij. Leibnizova formula omogoči integracijo funkcij, ki na zaprtem intervalu niso nujno povsod definirane. Sledi uvedba izlimitiranih integralov, ki sploh ne razširijo množice integrabilnih funkcij. Kot glavni izsledek navedemo izrek o monotoni konvergenci, ki poda zelo obvladljivo karakterizacijo funkcijskih zaporedij, za katera lahko zamenjamo vrstni red limite in integracije.

Keywords

Riemannov integral;Henstock-Kurzweilov integral;Leibnizova formula;izlimitirani integral;izrek o monotoni konvergenci;

Data

Language:	Slovenian
Year of publishing:	2024
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[M. Jerič]
UDC:	517
COBISS:	207995139
Views:	44
Downloads:	12
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Henstock-Kurzweil integral
Secondary abstract:	In this thesis we look at the Henstock-Kurzweil integral. Its definition is similar to Riemann’s, except that the fineness of the partition of intervals is determined by a function $\delta$ and no longer by a constant. This difference allows one to integrate much more general functions. Leibniz’s formula allows the integration of functions which are not necessarily defined everywhere on a closed interval. This is followed by the introduction of improper integrals, which do not extend the set of integrable functions at all. The main result is the monotone convergence theorem, which gives a very manageable characterisation of function sequences for which the order of limit and integration can be reversed.
Secondary keywords:	Riemann integral;Henstock-Kurzweil integral;Leibniz formula;improper integral;monotone convergence theorem;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	37 str.
ID:	25050668