A NEW APPROACH TO EGOROV’S THEOREM BY MEANS OF 𝛼𝛽-STATISTICAL IDEAL CONVERGENCE

Abstract

In this work, we introduce the 𝛼𝛽-statistical pointwise ideal convergence, 𝛼𝛽-statistical uniform ideal convergence, and 𝛼𝛽-equi-statistical ideal convergence for sequences of fuzzy-valued functions. With the help of some examples, we present the relationship between these convergence concepts. Moreover, we give the 𝛼𝛽-statistical ideal version of Egorov’s theorem for the sequences of fuzzy valued measurable functions.

Keywords

• egorov’s theorem
• 𝛼𝛽-statistical pointwise ideal convergence
• 𝛼𝛽-statistical uniform ideal convergence
• 𝛼𝛽-statistical equi-ideal convergence