scholarly journals On Riesz product measures; mutual absolute continuity and singularity

1988 ◽  
Vol 38 (2) ◽  
pp. 63-93 ◽  
Author(s):  
Shelby J. Kilmer ◽  
Sadahiro Saeki
Keyword(s):  
Absolute Continuity ◽  
Riesz Product ◽  
Product Measures

scholarly journals Absolute continuity, singularity and product measures

1982 ◽  
Vol 5 (4) ◽  
pp. 793-807
Author(s):  
Roy A. Johnson
Keyword(s):  
Absolute Continuity ◽  
Decomposition Theorem ◽  
Absolutely Continuous ◽  
Weakly Singular ◽  
Lebesgue Type Decomposition ◽  
Product Measures ◽  
Type Decomposition

Conditions are given under which a product of two semifinite measures is absolutely continuous or weakly singular with respect to another product of two semifinite measures. A Lebesgue type decomposition theorem is proved for certain product measures so that the resulting measures are themselves product measures.

scholarly journals Lp-convergence of a certain class of product martingales

1994 ◽  
Vol 37 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Stamatis Koumandos
Keyword(s):  
Sufficient Conditions ◽  
Real Numbers ◽  
Positive Real ◽  
Riesz Product ◽  
Product Measures ◽  
Nikodym Derivative

We establish the Kakutani dichotomy property for two generalized Rademacher–Riesz product measures μ, ν that either μ, ν are equivalent measures or they are mutually singular according as a certain series converges or diverges. We further give sufficient conditions so that in the equivalence case the Radon–Nikodym derivative dμ/dν belongs to Lp(v) for all positive real numbers p, by proving that a certain product martingale converges in Lp(v) for p ≧ 1.

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