A non absolutely convergent integral which admits transformation and can be used for integration on manifolds
Jiří Jarník; Jaroslav Kurzweil
Czechoslovak Mathematical Journal (1985)
- Volume: 35, Issue: 1, page 116-139
- ISSN: 0011-4642
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topJarník, Jiří, and Kurzweil, Jaroslav. "A non absolutely convergent integral which admits transformation and can be used for integration on manifolds." Czechoslovak Mathematical Journal 35.1 (1985): 116-139. <http://eudml.org/doc/13497>.
@article{Jarník1985,
author = {Jarník, Jiří, Kurzweil, Jaroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {integration on manifolds; non-absolute integrals; Riemann-type integral; Stokes theorem for differentiable vector fields},
language = {eng},
number = {1},
pages = {116-139},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A non absolutely convergent integral which admits transformation and can be used for integration on manifolds},
url = {http://eudml.org/doc/13497},
volume = {35},
year = {1985},
}
TY - JOUR
AU - Jarník, Jiří
AU - Kurzweil, Jaroslav
TI - A non absolutely convergent integral which admits transformation and can be used for integration on manifolds
JO - Czechoslovak Mathematical Journal
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 1
SP - 116
EP - 139
LA - eng
KW - integration on manifolds; non-absolute integrals; Riemann-type integral; Stokes theorem for differentiable vector fields
UR - http://eudml.org/doc/13497
ER -
References
top- J. Mawhin, Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields, Czechoslovak Math. J. 31 (106) (1981), No. 4, 614-632. (1981) Zbl0562.26004MR0631606
- J. Jarník J. Kurzweil Š. Schwabik, On Mawhin's approach to multiple nonabsolutely convergent integral, Časopis pro pěst. mat. 108 (1983), No. 4, 356-380. (1983) MR0727536
- J. Kurzweil, Nichtabsolut konvergente Integrale, Teubner-Texte für Mathematik 26, Teubner, Leipzig 1980. (1980) Zbl0441.28001MR0597703
- J. Jarník J. Kurzweil, A nonabsolutely convergent integral in which admits -transfor- mations, Časopis pro pěst. mat. 109 (1984), N0. 2, 157-167. (1984) MR0744873
- S. Sternberg, Lectures on Differential Geometry, Prentice-Hall Inc., Englewood Cliffs, N.J. 1964. (Russian translation: Mir, Moskva 1970) (1964) Zbl0129.13102MR0193578
- M. Spivak, Calculus on Manifolds, W. A. Benjamin Inc., New York-Amsterdam 1965. (Russian translation: Mir, Moskva 1968) (1965) Zbl0141.05403MR0209411
Citations in EuDML Documents
top- Jiří Jarník, Jaroslav Kurzweil, A new and more powerful concept of the PU-integral
- Jaroslav Kurzweil, Jean Mawhin, Washek Frank Pfeffer, An integral defined by approximating partitions of unity
- Giuseppa Riccobono, A PU-integral on an abstract metric space
- Wolfgang B. Jurkat, D. J. F. Nonnenmacher, A Hake-type property for the -integral and its relation to other integration processes
- V. Marraffa, A scalar Volterra derivative for the PoU-integral
- W. Jurkat, D. Nonnenmacher, An axiomatic theory of non-absolutely convergent integrals in Rn
- Wolfgang B. Jurkat, The divergence theorem and Perron integration with exceptional sets
- Jean Mawhin, Nonstandard analysis and generalized Riemann integrals
- Wolfgang B. Jurkat, D. J. F. Nonnenmacher, The fundamental theorem for the -integral on more general sets and a corresponding divergence theorem with singularities
- Jan Malý, Washek Frank Pfeffer, Henstock-Kurzweil integral on sets
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