On integrals with integrators in BV p
n 1936, L. C. Young proved that the Riemann-Stieltjes integral\int^b_a f dg exists, if f\in BV_p,\,g\in BV_q, \frac{1}{p}+\frac{1}{q}>1 and f,g do not have common discontinuous points. In this note, using Henstock's approach, we prove that \int^b_a f dg still exists without assuming the cond...
Gespeichert in:
Veröffentlicht in: | Real analysis exchange 2004, Vol.30 (no. 1), p.193-200 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | n 1936, L. C. Young proved that the Riemann-Stieltjes integral\int^b_a f dg
exists, if f\in BV_p,\,g\in BV_q, \frac{1}{p}+\frac{1}{q}>1 and f,g do not
have common discontinuous points. In this note, using Henstock's approach, we
prove that \int^b_a f dg still exists without assuming the condition on
discontinuous points. Some convergence theorems are also proved. |
---|---|
ISSN: | 1930-1219 |