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Some Remarks on Indicatrices of Measurable Functions

Marcin Kysiak (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

The sum of periodic functions

Stefano Mortola, Roberto Peirone (1999)

Bollettino dell'Unione Matematica Italiana

Si prova che ogni polinomio in una variabile reale di grado n è somma di n + 1 funzioni periodiche, ovviamente non tutte continue, e che ci sono funzioni di una variabile reale che non sono somma di un numero finito di funzioni periodiche.

Theory of rapid variation on time scales with applications to dynamic equations

Jiří Vítovec (2010)

Archivum Mathematicum

In the first part of this paper we establish the theory of rapid variation on time scales, which corresponds to existing theory from continuous and discrete cases. We introduce two definitions of rapid variation on time scales. We will study their properties and then show the relation between them. In the second part of this paper, we establish necessary and sufficient conditions for all positive solutions of the second order half-linear dynamic equations on time scales to be rapidly varying. Note...

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