Abstract
In this study, it was first shown that the intersection of a countably large number of ν-measurable sets and their union under some conditions are also ν-measurable. Besides , the relevant theorems were obtained, by giving non-Newtonian set definitions ■(ν@)G_δ and ■(ν@)F_σ. In addition, the Cantor perfect set was defined in a non-Newtonian sense, and the Cantor set, which is an important example in measure theory being uncountable but has zero measure, was generalized in a non-Newtonian sense.
References
- Çakmak, A. F., & Başar, F. (2012). Some new results on sequence spaces with respect to non-Newtonian calculus. Journal of Inequalities and Applications(228), 1-12.
- Demir, S. (2019). Reel Sayılarda Newtonyen Olmayan Lebesgue Ölçüsünün Bazı Özellikleri. Giresun: Giresun Üniversitesi Fen Bilimleri Enstitüsü.
- Duyar, C., & Oğur, O. (2017). A Note On Topology Of Non-Newtonian Real Numbers. Journal of Mathematics(13), 11-14.
- Duyar, C., & Sağır, B. (2017). Non-Newtonian Comment of Lebesgue Measure in Real Numbers. Journal of Mathematics, 1-4.
- Grossman, M., & Robert, K. (1972). Non-Newtonian Calculus. Pigeon Cove(Lowell Technological Institue).
- Grossmann, M. (1979). The first nonlinear system of differential and integral calculus. Galileo Institute.
- Grossmann, M. (1983). Bigeometric Calculus: A System with a Scale-Free Deriative. Archimedes Foundation, Rockport Massachussets.
- Oğur, O., & Demir, S. (2019). Newtonyen Olmayan Lebesgue Ölçüsü. Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 134-139.
- Oğur, O., & Demir, S. (2019). On non-Newtonian measure for α−closed sets. New Trends in Mathematical Sciences, 7(2), 202-207.
Abstract
Bu çalışmada, ilk olarak sayılabilir çoklukta ν-ölçülebilir kümenin kesişiminin ve bazı koşullar altında birleşiminin de ν-ölçülebilir olduğu gösterildi. Bunun yanında Newtonyen olmayan ■(ν@)G_δ ve ■(ν@)F_σ küme tanımları verilerek, ilgili teoremler elde edildi. Ayrıca Newtonyen olmayan anlamda Cantor mükemmel küme tanımlandı ve ölçü teorisinde önemli örneklerden olan sayılamaz fakat ölçüsü sıfır olan Cantor kümesi Newtonyen olmayan anlamda genelleştirildi.
References
- Çakmak, A. F., & Başar, F. (2012). Some new results on sequence spaces with respect to non-Newtonian calculus. Journal of Inequalities and Applications(228), 1-12.
- Demir, S. (2019). Reel Sayılarda Newtonyen Olmayan Lebesgue Ölçüsünün Bazı Özellikleri. Giresun: Giresun Üniversitesi Fen Bilimleri Enstitüsü.
- Duyar, C., & Oğur, O. (2017). A Note On Topology Of Non-Newtonian Real Numbers. Journal of Mathematics(13), 11-14.
- Duyar, C., & Sağır, B. (2017). Non-Newtonian Comment of Lebesgue Measure in Real Numbers. Journal of Mathematics, 1-4.
- Grossman, M., & Robert, K. (1972). Non-Newtonian Calculus. Pigeon Cove(Lowell Technological Institue).
- Grossmann, M. (1979). The first nonlinear system of differential and integral calculus. Galileo Institute.
- Grossmann, M. (1983). Bigeometric Calculus: A System with a Scale-Free Deriative. Archimedes Foundation, Rockport Massachussets.
- Oğur, O., & Demir, S. (2019). Newtonyen Olmayan Lebesgue Ölçüsü. Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 134-139.
- Oğur, O., & Demir, S. (2019). On non-Newtonian measure for α−closed sets. New Trends in Mathematical Sciences, 7(2), 202-207.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Computer Software |
| Journal Section | Articles |
| Authors | |
| Publication Date | March 15, 2024 |
| Submission Date | December 15, 2023 |
| Acceptance Date | March 5, 2024 |
| Published in Issue | Year 2024 Volume: 14 Issue: 1 |
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.