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A comparison of three recent selection theorems

Caterina Maniscalco (2007)

Mathematica Bohemica

We compare a recent selection theorem given by Chistyakov using the notion of modulus of variation, with a selection theorem of Schrader based on bounded oscillation and with a selection theorem of Di Piazza-Maniscalco based on bounded $𝒜, Λ$ -oscillation.

A descriptive definition of a BV integral in the real line

Diana Caponetti, Valeria Marraffa (1999)

Mathematica Bohemica

A descriptive characterization of a Riemann type integral, defined by BV partition of unity, is given and the result is used to prove a version of the controlled convergence theorem.

A necessary condition for HK-integrability of the Fourier sine transform function

Juan H. Arredondo, Manuel Bernal, Maria G. Morales (2025)

Czechoslovak Mathematical Journal

The paper is concerned with integrability of the Fourier sine transform function when $f \in {BV}_{0} (ℝ)$ , where ${BV}_{0} (ℝ)$ is the space of bounded variation functions vanishing at infinity. It is shown that for the Fourier sine transform function of $f$ to be integrable in the Henstock-Kurzweil sense, it is necessary that $f / x \in L^{1} (ℝ)$ . We prove that this condition is optimal through the theoretical scope of the Henstock-Kurzweil integration theory.

A note on the difference property.

Norbert Brunner (1982)

Collectanea Mathematica

An application of the generalized Maligranda–Orlicz's Lemma.

Castillo, René Erlín, Trousselot, Eduard (2008)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

An integral defined by approximating $B V$ partitions of unity

Jaroslav Kurzweil, Jean Mawhin, Washek Frank Pfeffer (1991)

Czechoslovak Mathematical Journal

Area functionals and Godbillon-Vey cocycles

Takashi Tsuboi (1992)

Annales de l'institut Fourier

We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.