On A Recent Characterization of Baire Class One Functions

Jonald Fenecios

Abstract


Recently, a new characterization of Baire class one functions is given based on the countable decomposition of their set of points of discontinuity which improves a theorem by Henri Lebesgue. The proof makes use of the $\epsilon$-$\delta$ characterization of Baire class one functions. In this note, we shall give another proof of this result that avoids the use of the $\epsilon$-$\delta$ characterization. Furthermore, we use the theorem in finding applications involving the class of cliquish functions.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|