Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R.G. Bartle, N. Dunford, J. Schwartz, Weak compactness and vector measures, Can. J. Math., 7(1955), 289–305.
G. Birkoff, Lattice theory, 2nd. ed., AMS Colloquium Publications (1948).
C.H. Brook, Decomposition of submeasures, Preprint.
C.H. Brook, T. Traynor, The boolean algebra of exhaustive Fréchet-Nikodým topologies and the Lebesgue Decomposition, Univ. of Windsor Mathematics Report, 83-14.
L. Drewnowski, Topological rings of sets, continuous set functions, integration I, II, III, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 20(1972), 269–276, 277–286, 439–445.
L. Drewnowski, On control submeasures and measures, Studie Math., 50(1974), 203–224.
T.P. Dence., Can. J. Math. 29 (1977), 295–298.
I. Fleischer, Extending group-valued modular functions on lattice CRM-525 (1975), Univ. de Montréal)
I. Fleischer, A Lebesgue decomposition for group-valued functions on a lattice, CRM-735(1977), Université de Montréal.
G. fox and P. Morales, Strongly additive functions on lattices, Fund. Math. 78(1973),99–108.
I. Fleischer and T. Traynor, Equivalence of Group-valued measures on an abstract lattice, Bull. Acad. Pol. Sci. 28(1980), 549–556.
I. Fleischer, T. Traynor, Group-valued modular functions, Alg. Universalis, 14(1982),287–291.
L. Geissinger, Valuations on distributive lattices I, Arch. Math. 24(1973),230–239.
P. Kranz, Mutual equivalence of vector and scalar measures on lattices, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron. Phys. 25(1977), 243–250.
P. Kranz, Extension of valuation on a lattice, fund. Math. 91(1976).
Z. Lipecki, On strongly additive set functions, Colloq. Math., (1971), 255–256, MR, 43(1972), 7586.
C.E. Rickart, Decomposition of additive set functions, Duke Math. J., 10(1943),653–665.
V.I. Rybakov, On a theorem of Bartle-Dunford-Schwarz concerning vector measures, Math. Zametki, 7(1970), 247–254, translated in Math. Notes, 7(1970), 147–151.
M.F. Smiley, An extension of metric distributive lattices with an application in general analysis, Trans. A.M.S., 56(1944), 435–447.
M. Takesaki, Theory of Operator Algebras I, Springer (1979), New York.
T. Traynor, S-bounded additive set functions, in: Vector and operator valued measures and applications, Academic Press, 1973, 340–350.
H. Weber, Topological Boolean rings. Decomposition of finitely additive set functions, Pacific J. Math. 109(1983).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Traynor, T. (1984). Modular functions and their Frechet-Nikodym topologies. In: Kölzow, D., Maharam-Stone, D. (eds) Measure Theory Oberwolfach 1983. Lecture Notes in Mathematics, vol 1089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072613
Download citation
DOI: https://doi.org/10.1007/BFb0072613
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13874-7
Online ISBN: 978-3-540-39069-5
eBook Packages: Springer Book Archive