An Answer to Some Questions of Ene

Sworowski, Piotr

doi:10.14321/realanalexch.30.1.0183

Cited by 3 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is an approximately continuous ACG-function F defined on [0, 1] such that µ F and µ F differ for some subsets of D ap F . We take the function from Example 3.1 of [24]. Notice that the (countable) set {x…”

Section: -Representations Of µ Fmentioning

confidence: 99%

On some variational measures related to the wide Denjoy integral and its counterparts

Sworowski¹

2019

Rend. Sem. Mat. Univ. Padova

View full text Add to dashboard Cite

Weak and q-weak variational measures defined by Brian S. Thomson [On VBG functions and the Denjoy-Khintchine integral, Real Analysis Exchange, 41(1) (2015/16), 173-226] are shown to coincide with variational measures resulting from Riemann definitions of some wide Denjoy type integrals. This fact is applied in characterizations of these integrals, via absolute continuity of weak and q-weak measures. In related results, it is discussed if these Riemann definitions can be essentially simplified. The paper is a follow-up to a paper by the author published some time ago in the Rendiconti [On Riemann-type definition for the wide Denjoy integral, Rendiconti del Seminario Matematico della Università di Padova, 126 (2011), 175-200].

show abstract

Section: -Representations Of µ Fmentioning

confidence: 99%

On some variational measures related to the wide Denjoy integral and its counterparts

Sworowski¹

2019

Rend. Sem. Mat. Univ. Padova

View full text Add to dashboard Cite

show abstract

“…These integrals, at the cost of more sophisticated proof of monotonicity property, were easier to show to cover the AP-integral. The classes L i , i = 1, 2, 3, 4, do not coincide, so do the corresponding classes of integrands (see [49], [58]). Chart 1, borrowed from [58], depicts interrelations between them.…”

Section: Burkill's Ap-integralmentioning

confidence: 99%