ABSTRACT
It is well known that one of the earliest important results in real analysis and Lebesgue measure theory was obtained by Egorov [50] who discovered close relationships between the uniform convergence and the convergence almost everywhere of a sequence of real-valued Lebesgue measurable functions. This classical result (known now as the Egorov theorem) has numerous consequences and applications in analysis. For example, it suffices to mention that another classical result in real analysis, the so-called Luzin theorem on the structure of Lebesgue measurable functions, can easily be deduced by starting with the Egorov theorem.
