İstatistiksel Epi-Yakınsaklık ile İlgili Temel Özellikler

Bu çalışmada, istatistiksel epi-yakınsaklığın sonraki çalışmalarda daha verimli kullanılabilmesi için bazı temel özelliklere yer verildi. Bir fonksiyon dizisinin düzgün istatistiksel yakınsaklık durumu, fonksiyon dizilerinin bileşkesinin istatistiksel epi-limiti, fonksiyon dizilerinin toplamının istatistiksel epi-limiti, fonksiyon dizisinin alttan yarı sürekli olması halinde epi-limit fonksiyonunun özelliği ve fonksiyon dizisindeki her bir fonksiyonun konveks olması halinde epi-limit fonksiyonunun konveksliği gibi durumlar çalışıldı.

Basic Properties of Statistical Epi-Convergence

In this paper, we give some basic properties in order to use statistical epi-convergence more efficientlyin future studies. Such situations are studied: Uniform statistical convergence of sequence of functions,statistical epi-limit of compound of sequence of functions, statistical epi-limit of the sum of sequence offunctions, the property of epi-limit function if the sequence of functions are lower semi-continuous andthe convexity of epi-limit function if each function in the sequence is convex.

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