A Note on Non-Newtonian Measurable Sets

Oğuz Oğur

Makale detayları

A Note on Non-Newtonian Measurable Sets

Yazarlar:

Oğuz Oğur

Yayıncı:

Giresun University

Ana Başlıklar:

Bilgisayar Yazılımı

Dergi:

Karadeniz Fen Bilimleri Dergisi Vol.14 Issue 1, pp.295-303

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

Türkçe

Document ID (Org No.):

2001313219

pISSN:

2564-7377

Anahtar kelimeler:

Özet:

 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 νG_δ and νF_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.

 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 νG_δ and νF_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.

 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 νG_δ and νF_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.

 Bu çalışmada, ilk olarak sayılabilir çoklukta ν-ölçülebilir kümenin kesişiminin ve bazı koşullar altında birleşiminin de ν-ölçülebilir olduğu gösterildi. Bunun yanında Newtonyen olmayan νG_δ ve νF_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.

Makale detayları

A Note on Non-Newtonian Measurable Sets

Yazarlar:

Oğuz Oğur

Yayıncı:

Giresun University

Ana Başlıklar:

Bilgisayar Yazılımı

Dergi:

Karadeniz Fen Bilimleri Dergisi Vol.14 Issue 1, pp.295-303

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

Türkçe

Document ID (Org No.):

2001313219

pISSN:

2564-7377

Non-Newtonian Measure

ν-measurable set

ν-Cantor SetNewtonyen Olmayan Ölçü

ν-ölçülebilir küme

ν-Cantor Küme

Sayı

Makale detayları

A Note on Non-Newtonian Measurable Sets

Yazarlar: Oğuz Oğur

Yayıncı: Giresun University

Ana Başlıklar: Bilgisayar Yazılımı

Dergi: Karadeniz Fen Bilimleri Dergisi Vol.14 Issue 1, pp.295-303

Belge Tipi: Makale

Yayın Tarihi: 3/2024

Belge Dili: Türkçe

Document ID (Org No.): 2001313219

pISSN: 2564-7377

Non-Newtonian Measure

ν-measurable set

ν-Cantor SetNewtonyen Olmayan Ölçü

ν-ölçülebilir küme

ν-Cantor Küme

Sayı

Yazarlar:

Oğuz Oğur

Yayıncı:

Giresun University

Ana Başlıklar:

Bilgisayar Yazılımı

Dergi:

Karadeniz Fen Bilimleri Dergisi Vol.14 Issue 1, pp.295-303

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

Türkçe

Document ID (Org No.):

2001313219

pISSN:

2564-7377