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#### Mathelogician

##### Member

- Aug 6, 2012

- 35

He

**Defines**the notions of increasing and decreasing sequences of sets (here sets of events) and then

**defines**infinite limits of such sequences (as infinite union and infinite intersection of the sets of events; respectively) and then he claims proving the continuity of f using a way the following classic theorem of calculus:

f :

**R**-> R is continuous on R if and only if, for every convergent sequence {xn} n =1 to infinite in R, limf({xn})=f(lim{xn}) as n goes to infinity.

But

1-the classic theorem is for functions from R to R; how can he use it for a set function (which is from a collection of sets to R, here)

2- Even if he is right, he only proves the continuity of the cases of increasing and decreasing sequences; not convergent(which he has not defined!!) in general.

Now what to do with this problem?!

Regards.