On Fréchet theorem in the set of measure preserving functions over the unit interval
In this paper, we study the Fréchet theorem in the set of measure preserving functions over the unit interval and show that any measure preserving function on [0,1] can be approximated by a sequence of measure preserving piecewise linear continuous functions almost everywhere. Some application is in...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000552 |
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| _version_ | 1849686124420661248 |
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| author | So-Hsiang Chou Truc T. Nguyen |
| author_facet | So-Hsiang Chou Truc T. Nguyen |
| author_sort | So-Hsiang Chou |
| collection | DOAJ |
| description | In this paper, we study the Fréchet theorem in the set of measure preserving functions over the unit interval and show that any measure preserving function on [0,1] can be approximated by a sequence of measure preserving piecewise linear continuous functions almost everywhere. Some application is included. |
| format | Article |
| id | doaj-art-b8c2fa2c12f24b4bb1dcc5fd886fc481 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b8c2fa2c12f24b4bb1dcc5fd886fc4812025-08-20T03:22:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113237337810.1155/S0161171290000552On Fréchet theorem in the set of measure preserving functions over the unit intervalSo-Hsiang Chou0Truc T. Nguyen1Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403-0221, Ohio, USADepartment of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403-0221, Ohio, USAIn this paper, we study the Fréchet theorem in the set of measure preserving functions over the unit interval and show that any measure preserving function on [0,1] can be approximated by a sequence of measure preserving piecewise linear continuous functions almost everywhere. Some application is included.http://dx.doi.org/10.1155/S0161171290000552measure preservingBorel setdistribution functionspline. |
| spellingShingle | So-Hsiang Chou Truc T. Nguyen On Fréchet theorem in the set of measure preserving functions over the unit interval International Journal of Mathematics and Mathematical Sciences measure preserving Borel set distribution function spline. |
| title | On Fréchet theorem in the set of measure preserving functions over the unit interval |
| title_full | On Fréchet theorem in the set of measure preserving functions over the unit interval |
| title_fullStr | On Fréchet theorem in the set of measure preserving functions over the unit interval |
| title_full_unstemmed | On Fréchet theorem in the set of measure preserving functions over the unit interval |
| title_short | On Fréchet theorem in the set of measure preserving functions over the unit interval |
| title_sort | on frechet theorem in the set of measure preserving functions over the unit interval |
| topic | measure preserving Borel set distribution function spline. |
| url | http://dx.doi.org/10.1155/S0161171290000552 |
| work_keys_str_mv | AT sohsiangchou onfrechettheoreminthesetofmeasurepreservingfunctionsovertheunitinterval AT tructnguyen onfrechettheoreminthesetofmeasurepreservingfunctionsovertheunitinterval |