|
The representation of abstract measure functions
Author:
Dorothy Maharam
Journal:
Trans. Amer. Math. Soc. 65 (1949), 279-330
MSC:
Primary 27.2X
MathSciNet review:
0028923
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- [1]
S. Banach and A. Tarski, Sur les décompositions dénombrables, Fund. Math. vol. 6 (1924) pp. 244-277.
- [2]
Garrett
Birkhoff, Lattice theory, American Mathematical Society
Colloquium Publications, Vol. XXV, American Mathematical Society,
Providence, R.I., 1961. Revised ed. MR 0123490
(23 #A815)
- [3]
Garrett
Birkhoff, Moore-Smith convergence in general topology, Ann. of
Math. (2) 38 (1937), no. 1, 39–56. MR
1503323, http://dx.doi.org/10.2307/1968508
- [4]
Gustave
Choquet, Préliminaires à une nouvelle
définition de la mesure, C. R. Acad. Sci. Paris
215 (1942), 52–54 (French). MR 0009617
(5,174b)
- [5]
Gustave
Choquet, Choix d’une mesure cartésienne Δ.
Applications, C. R. Acad. Sci. Paris 215 (1942),
101–103 (French). MR 0009618
(5,174c)
- [6]
H. Freudenthal, Teilweise geordnete Moduln, K. Akademie van Wetenschappen, Afdeeling Natuurkunde, Proceedings of the Section of Sciences vol. 39 (1936) pp. 647-657.
- [7]
Paul
R. Halmos, The decomposition of measures, Duke Math. J.
8 (1941), 386–392. MR 0004718
(3,50e)
- [8]
E.
R. van Kampen, Infinite product measures and infinite
convolutions, Amer. J. Math. 62 (1940),
417–448. MR 0001282
(1,209d)
- [9]
L.
H. Loomis, On the representation of
𝜎-complete Boolean algebras, Bull.
Amer. Math Soc. 53
(1947), 757–760. MR 0021084
(9,20b), http://dx.doi.org/10.1090/S0002-9904-1947-08866-2
- [10]
Dorothy
Maharam, On measure in abstract sets,
Trans. Amer. Math. Soc. 51 (1942), 413–433. MR 0006594
(4,11d), http://dx.doi.org/10.1090/S0002-9947-1942-0006594-0
- [11]
Dorothy
Maharam, On homogeneous measure algebras, Proc. Nat. Acad.
Sci. U. S. A. 28 (1942), 108–111. MR 0006595
(4,12a)
- [12]
F.
J. Murray and J.
Von Neumann, On rings of operators, Ann. of Math. (2)
37 (1936), no. 1, 116–229. MR
1503275, http://dx.doi.org/10.2307/1968693
- [13]
J.
von Neumann, Zur Operatorenmethode in der klassischen
Mechanik, Ann. of Math. (2) 33 (1932), no. 3,
587–642 (German). MR
1503078, http://dx.doi.org/10.2307/1968537
- [14]
G.
Baley Price, The theory of integration, Trans. Amer. Math. Soc. 47 (1940), 1–50. MR 0001442
(1,239d), http://dx.doi.org/10.1090/S0002-9947-1940-0001442-5
- [15]
M.
H. Stone, The theory of representations for
Boolean algebras, Trans. Amer. Math. Soc.
40 (1936), no. 1,
37–111. MR
1501865, http://dx.doi.org/10.1090/S0002-9947-1936-1501865-8
- [1]
- S. Banach and A. Tarski, Sur les décompositions dénombrables, Fund. Math. vol. 6 (1924) pp. 244-277.
- [2]
- G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloquium Publications, vol. 25, 1940. MR 0123490 (23:A815)
- [3]
- -, Moore-Smith convergence in general topology, Ann. of Math. vol. 38 (1937) pp. 39-56. MR 1503323
- [4]
- G. Choquet, Préliminaires à une nouvelle définition de la mesure, C. R. Acad. Sci. Paris vol. 215 (1942) pp. 52-54. MR 0009617 (5:174b)
- [5]
- -, Choix d'une mesure cartésienne
; applications, C. R. Acad. Sci. Paris vol. 215 (1942) pp. 101-103. MR 0009618 (5:174c)
- [6]
- H. Freudenthal, Teilweise geordnete Moduln, K. Akademie van Wetenschappen, Afdeeling Natuurkunde, Proceedings of the Section of Sciences vol. 39 (1936) pp. 647-657.
- [7]
- P. Halmos, The decomposition of measures, Duke Math. J. vol. 8 (1941) pp. 386-392. MR 0004718 (3:50e)
- [8]
- E. R. van Kampen, Infinite product measures and convolutions, Amer. J. Math. vol. 62 (1940) pp. 417-448. MR 0001282 (1:209d)
- [9]
- L. H. Loomis, On the representation of
-complete Boolean algebras, Bull. Amer. Math. Soc. vol. 53 (1947) pp. 757-760. MR 0021084 (9:20b)
- [10]
- D. Maharam, On measure in abstract sets, Trans. Amer. Math. Soc. vol. 51 (1942) pp. 413-433. MR 0006594 (4:11d)
- [11]
- -, On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. vol. 28 (1942) pp. 108-111. MR 0006595 (4:12a)
- [12]
- F. J. Murray and J. von Neumann, On rings of operators, Ann. of Math. vol. 37 (1936) pp. 116-229. MR 1503275
- [13]
- J. von Neumann, Zur Operatorenmethode in der klassischen Mechanik, Ann. of Math. vol. 33 (1932) pp. 587-642. MR 1503078
- [14]
- G. B. Price, The theory of integration, Trans. Amer. Math. Soc. vol. 47 (1940) pp. 1-50. MR 0001442 (1:239d)
- [15]
- M. H. Stone, The theory of representation for Boolean algebras, Trans. Amer. Math. Soc. vol.40 (1936) pp. 37-111. MR 1501865
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC:
27.2X
Retrieve articles in all journals
with MSC:
27.2X
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1949-0028923-0
PII:
S 0002-9947(1949)0028923-0
Article copyright:
© Copyright 1949 American Mathematical Society
|