Si introducono integrali propri e impropri per funzioni $:X \to S =$ semigruppo commutativo con metrica generalizzata rispetto a una biaddiva $\Phi : S \times \Omega \to S^{\prime}$ di variazione finita; $\Omega$ è un semianello di insiemi $\subset X$. Per il caso proprio si usa una riformulazione della definizione di Riemann, per l’improprio si applica convergenza locale in misura assieme a convergenza in media.
Referenze Bibliografiche
[5]
K. Bichteler (
1973) -
Integration Theory,
«Lecture Notes in Math.»,
313, Berlin-Heidelberg-New York:
Springer. |
Zbl 0249.28002[6]
J.K. Brooks (
1968) -
An integration theory for set-valued measures, I,
«Bull. Soc. Roy. Sci.», Liege
37, 312-319. |
MR 235091[8] N. Dunford (1967) - Schwartz J.T. (1967) - Linear Operators. I. 4th printing New York: Interscience.
[11]
H. Günzler (
1971) -
Integration.
Lecture notes, Univ. Kiel. |
Zbl 0241.20001[12] H. Günzler (1975) - Unconditional finitely additive integration, «Mimeographed. Math. Sem. Univ.», Kiel.
[13] H. Günzler (1975) - Integral representations with prescribed lattices, «Rend. Sem. Mat. Fis.», Milano XLV, 107-168.
[14]
K. Iseki (
1964) -
An approach to locally convex topological linear spaces,
«Proc. Jap. Ac.»,
40, 818-820. |
MR 179574 |
Zbl 0132.08702[15]
N. Jacobson (
1964) -
Lectures in abstract algebra. III. New York:
van Nostrand. |
MR 172871[16] B. Juckel (1975) - Riemann-integrierbare Funktionen und obere Normen, «Diplomarbeit, Math. Sem.», Univ. Kiel.
[17]
A. Kirsch (
1952) -
Über Zerlegungsgleichheit von Funktionen und Integration...,
«Math. Ann.»,
24, 343-363. |
fulltext EuDML |
Zbl 0047.29201[18] G. Köthe (1969) - Topological Vector Spaces I. Berlin: Springer.
[20]
W.A.J. Luxemburg (
1961) -
The abstract Riemann integral and... repeated integrals. Ia. Ib.
«Indag. Math.»,
23, 516-545. |
Zbl 0109.03801[21]
W.A. Luxemburg,
A.C. Zaanen (
1971) -
Riesz spaces. I. Amsterdam,
«North-Holland Publ. Co.». |
MR 511676[22]
H. Matzinger (
1967) -
Verallgemeinerte Normen in topologischen Gruppen und Vektorräumen,
«Comm. math. Helv.»,
41, 307-3I2. |
fulltext (doi) |
MR 208340[24]
A.F. Monna (
1970) -
Analyse non-archimedienne. Berlin:
Springer. |
MR 295033[25]
A.S. Nemirovskii,
M. Yu Ocan,
R. Redzuani (
1972) -
Conditions for Riemann integrability of functions with values in a Banach space (Russian).
Vestnik Mosk. Univ. 27, 62-65. |
MR 308360[26]
R. Redzuani (
1971) -
On the question of Riemann-integrability..., (Russ.),
Vestnik Moskov Univ. Ser. I.
«Math. Meh.»,
26, 75-79. |
MR 293055[27]
J. Ridder (
1968) -
Die allgemeine Riemann-Integration in topologischen Räumen A-D,
«Indag. Math.»,
30, 12-23, 137-148, 239-252, 363-377. |
MR 239043 |
Zbl 0155.10301[28] H.H. Schäfer (1971) - Topological Vector Spaces, Berlin: Springer.
[31]
B.C. Strijdom (
1959) -
Abstract Riemann Integration. Assen:
Van Gorcum and Co.. |
Zbl 0084.05004[32]
M. Takahashi (
1971) -
An extension of an integral. I, II.
«Proc. Jap. Ac.»,
47, 257-261, 262-267. |
MR 293057 |
Zbl 0233.28010[33]
F. Topsøe (
1970) -
Topology and Measure,
«Lecture Notes in Math.»,
133, Berlin-Heidelberg-New York:
Springer. |
Zbl 0197.33301