Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-17T01:29:52.382Z Has data issue: false hasContentIssue false

Theorems of Novikov type

Published online by Cambridge University Press:  26 February 2010

Roy O. Davies
Affiliation:
The Department of Mathematics, The University,Leicester, LE1 7RH.
J. E. Jayne
Affiliation:
The Department of Mathematics, University College London, London, WC1E 6BT.
A. J. Ostaszewski
Affiliation:
The Department of Mathematics, The London School of Economics, London, WC2A 2AE.
C. A. Rogers
Affiliation:
The Department of Mathematics, University College London, London, WC1E 6BT.
Get access

Extract

Novikov [7] or [5, Th. 2, p. 510] proves that: if{An} is a sequence of analytic sets in a complete separable metric space and

then there is a sequence {Bn} of Borel sets with

Type
Research Article
Copyright
Copyright © University College London 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Frolik, Z.. “A contribution to the descriptive theory of sets and spaces”, in General Topology and its Relations to Analysis and Algebra (Academic Press, New York, 1962), pp. 157–73.Google Scholar
1.Frolik, Z.. “Baire sets that are Borelian subspaces ”, Proc. Royal Soc, A, 299 (1967), 287290.Google Scholar
1.Frolik, Z.. “Analytic and Borelian sets in general spaces”, Proc. London Math. Soc. (3), 21 (1970), 679692.Google Scholar
4.Kuratowski, K.. “Sur les théoremès de separation dans la théorie des ensembles ”, Fund. Math., 26 (1936), 183191.CrossRefGoogle Scholar
5.Kuratowski, K.. Topology, Vol. I (Academic Press, New York, 1966).Google Scholar
6.Meyer, P. A.. Probabilités et Potentiel (Hermann, Paris, 1966) or Probability and Potentials (Blaisdell, Boston, 1966).Google Scholar
7.Novikov, P. S.. “Sur la séparabilité-B dénombrable des ensembles analytiques ”, C.R. Acad. Sc, U.R.S.S., 2 (1934), 145148.Google Scholar
8.Novikov, P. S..“Généralisation du deuxième principe de séparabilité ”, CR.Acad.Sc, U.R.S.S, 4(1934), 811.Google Scholar
9.Kunugui, K.. “La théorie des ensembles analytiques et les espaces abstraits ”, J. Fac. Sci. Hokkaido Univ. Ser. I, 4 (1935), 140.Google Scholar
10.Liapounov, A.. “Séparabilité multiple pour le cas des opérations δs ”, C.R. Acad. Sc, U.R.S.S., 53 (1946), 395398.Google Scholar
11.Lusin, N.. Leçons sur les ensembles analytiques (Chelsea Pub. Co., New York, 1972).Google Scholar
12.Mokobodzki, G.. “Démonstration élémentaire d'un théorème de Novikov”, Séminaire de Probabilités, Springer–Verlag Lecture Notes in Maths., Vol. 511, 1976.Google Scholar
13.Ostaszewski, A. J.. “On Lusin's separation principle in Hausdorff spaces ”, Proc. London Math. Soc. (3), 27 (1973), 649666.CrossRefGoogle Scholar
14.Rogers, C. A.. “Analytic sets in Hausdorff spaces ”, Mathematika, 11 (1964), 18.CrossRefGoogle Scholar
15.Rogers, C. A.. “Lusin's first separation theorem ”, J . London Math. Soc. (2), 3 (1971), 103118.CrossRefGoogle Scholar
16.Rogers, C. A.. “Lusin's second separation theorem ”, J. London Math. Soc. (2), 6 (1973), 491503CrossRefGoogle Scholar
17.Rogers, C. A. and Willmott, R. C.. “On the projection of Souslin sets ”, Mathematika, 13 (1966), 147150.CrossRefGoogle Scholar
18.Raymond, J. Saint.“Boreliens a coupes Ka ”, Bull. Soc. Math. France, 104 (1976), 389400.Google Scholar
19.Sierpinski, W.. “Le théorème de Souslin dans la théworie générate des ensembles ”, Fund. Math., 25 (1935), 2932.CrossRefGoogle Scholar