Displaying similar documents to “Measurable Functions and Almost Continuous Functions.”

Almost Everywhere First-Return Recovery

Michael J. Evans, Paul D. Humke (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We present a new characterization of Lebesgue measurable functions; namely, a function f:[0,1]→ ℝ is measurable if and only if it is first-return recoverable almost everywhere. This result is established by demonstrating a connection between almost everywhere first-return recovery and a first-return process for yielding the integral of a measurable function.

Some Remarks on Indicatrices of Measurable Functions

Marcin Kysiak (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We show that for a wide class of σ-algebras 𝓐, indicatrices of 𝓐-measurable functions admit the same characterization as indicatrices of Lebesgue-measurable functions. In particular, this applies to functions measurable in the sense of Marczewski.

On measurable relation

C. Himmelberg, T. Parthasarathy, F. Van Vleck (1981)

Fundamenta Mathematicae

Similarity:

On the difference property of families of measurable functions

Rafał Filipów (2003)

Colloquium Mathematicae

Similarity:

We show that, generally, families of measurable functions do not have the difference property under some assumption. We also show that there are natural classes of functions which do not have the difference property in ZFC. This extends the result of Erdős concerning the family of Lebesgue measurable functions.