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ch6 2012/06/19 16:38 ch6 2012/06/19 16:39 aktuális
sorszám 8: sorszám 8:
4. On page 385 Example 6.36 one should use the fact that if there is an additive measure on an algebra which is regular with respect to a sigma compact system then it is sigma additive on the algebra therefore this measure has a sigma additive extension to the generated sigma algebra. One should observe that the cilinder sets which are compact when restricted to //C([0,t])// form a sigma compact system of sets in the space of continuous functions over the real line. The reason for this is that these cilinder sets are closed in the greater space, so one can use the usual diagonal procedure to find a continuous function in the intersection. If every finite intersection is non-empty one can assume that the sets are decreasing and one can select a function from every finite intersection. If the set of endpoints of the supporting time intervals is bounded then we can assume that after the supremum of the right endpoints all the selected functions are constant. 4. On page 385 Example 6.36 one should use the fact that if there is an additive measure on an algebra which is regular with respect to a sigma compact system then it is sigma additive on the algebra therefore this measure has a sigma additive extension to the generated sigma algebra. One should observe that the cilinder sets which are compact when restricted to //C([0,t])// form a sigma compact system of sets in the space of continuous functions over the real line. The reason for this is that these cilinder sets are closed in the greater space, so one can use the usual diagonal procedure to find a continuous function in the intersection. If every finite intersection is non-empty one can assume that the sets are decreasing and one can select a function from every finite intersection. If the set of endpoints of the supporting time intervals is bounded then we can assume that after the supremum of the right endpoints all the selected functions are constant.
-5. On page 394. in Theorem 6.46 one should assume that //U// contains the left limits of //X// as well.+5. On page 394. in Theorem 6.46 one should assume that //U// contains the left limits //X(t-)// as well.
6. On page 430. in formula (6.59) there is a latex error. One should delete [4pt]. 6. On page 430. in formula (6.59) there is a latex error. One should delete [4pt].
7. On page 448. in the proof of Proposition 6.94 one can use Fubini's theorem as //w// is continuous in the time variable, and as it is adapted it is product measurable so the set in the double integral is product measurable. The same argument is valid for every level set of //w//. 7. On page 448. in the proof of Proposition 6.94 one can use Fubini's theorem as //w// is continuous in the time variable, and as it is adapted it is product measurable so the set in the double integral is product measurable. The same argument is valid for every level set of //w//.
 
ch6.txt · Utolsó módosítás: 2012/06/19 16:39 szerkesztette: medvegyev
 
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