| Title:
|
A note on almost sure convergence and convergence in measure (English) |
| Author:
|
Kříž, P. |
| Author:
|
Štěpán, J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
29-40 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The present article studies the
conditions under which the almost
everywhere convergence and the
convergence in measure coincide.
An application in the statistical
estimation theory is outlined as
well. (English) |
| Keyword:
|
convergence in measure |
| Keyword:
|
almost sure convergence |
| Keyword:
|
pointwise compactness |
| Keyword:
|
Lusin property |
| Keyword:
|
strongly consistent estimators |
| MSC:
|
28A20 |
| MSC:
|
60B05 |
| MSC:
|
60F05 |
| MSC:
|
60F15 |
| MSC:
|
62C10 |
| MSC:
|
62F12 |
| idZBL:
|
Zbl 06383783 |
| idMR:
|
MR3160824 |
| . |
| Date available:
|
2014-01-17T09:32:45Z |
| Last updated:
|
2016-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143566 |
| . |
| Reference:
|
[1] Asanov M.O., Veličko N.V.: Kompaktnye množestva v $C_p(X)$.Comment. Math. Univ. Carolinae 22 (1981), 255–266. |
| Reference:
|
[2] Blackwell D.: There are no Borel SPLIFs.Ann. Probability 8 (1980), 1189–1190. Zbl 0451.28001, MR 0602393, 10.1214/aop/1176994581 |
| Reference:
|
[3] Dunford N., Schwartz J.T.: Linear Operators Part I: General Theory.John Wiley & Sons, Inc., New Jersey, 1988. Zbl 0635.47001, MR 1009162 |
| Reference:
|
[4] Fremlin D.H.: Measure Theory, Vol 4, Topological Measure Spaces.Colchester: Torres Fremlin, 2003. Zbl 1166.28001, MR 2462372 |
| Reference:
|
[5] Ionescu Tulcea A.: On pointwise convergence, compactness and equicontinuity I.Z. Wahrscheinlichkeitstheorie und verw. Gebiete 26 (1973), 197–205. MR 0405102, 10.1007/BF00532722 |
| Reference:
|
[6] Ionescu Tulcea A.: On pointwise convergence, compactness and equicontinuity II.Advances in Math. 12 (1974), 171–177. Zbl 0301.46032, MR 0405103, 10.1016/S0001-8708(74)80002-2 |
| Reference:
|
[7] Kelley J.L.: General Topology.Springer, New York, 1975. Zbl 0518.54001, MR 0370454 |
| Reference:
|
[8] Kříž P.: How to construct Borel measurable PLIFs?.WDS'11 Proc. of Contr. Papers, Part I, (2011), 43–48. |
| Reference:
|
[9] Štěpán J.: The probability limit identification function exists under the continuum hypothesis.Ann. Probability 1 (1973), 712–715. Zbl 0263.60013, MR 0356196, 10.1214/aop/1176996899 |
| . |
