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On strong liftings for projective limits

100%

Macheras N. D., Strauss W.

Fundamenta Mathematicae

1994

tom 144

nr 3

209-229

We discuss the permanence of strong liftings under the formation of projective limits. The results are based on an appropriate consistency condition of the liftings with the projective system called "self-consistency", which is fulfilled in many situations. In addition, we study the relationship of self-consistency and completion regularity as well as projective limits of lifting topologies.

Product liftings and densities with lifting invariant and density invariant sections

81%

Musiał K., Strauss W., Macheras N. D.

Fundamenta Mathematicae

2000

tom 166

nr 3

281-303

Given two measure spaces equipped with liftings or densities (complete if liftings are considered) the existence of product liftings and densities with lifting invariant or density invariant sections is investigated. It is proved that if one of the marginal liftings is admissibly generated (a subclass of consistent liftings), then one can always find a product lifting which has the property that all sections determined by one of the marginal spaces are lifting invariant (Theorem 2.13). For a large class of measures Theorem 2.13 is the best possible (Theorem 4.3). When densities are considered, then one can always have a product density with measurable sections, but in the case of non-atomic complete marginal measures there exists no product density with all sections being density invariant. The results are then applied to stochastic processes.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Macheras N. D.

2 Strauss W.

1 Musiał K.

1 2000

1 1994

Wyniki wyszukiwania

On strong liftings for projective limits

Product liftings and densities with lifting invariant and density invariant sections