50 
correspond to a common element of VV; and Vs, we obtain 
| Ly—L| cie+te+4e=e for every aggregate H corresponding 
to an element of Ws. 
6. Finally we prove, that the aggregate K (as regards the covering 
by the parts of VW) likewise has the limit L. We obtain: 
|\E—L| < |E—Lge| + [Le—-Ll, 
E being an element of G. Owing to the uniform convergence the 
positive number d, can be determined so, as to give |#—Lg|<he 
if 7 be an element of Go, i. e. corresponds to an element of Ws. At 
the same time we can d, determine so, as to obtain |Lg—L|<}e 
if G corresponds to an element of Vs. If now d be the smallest 
of the numbers d, and d,, then the inequality |H—L| << jet Jee 
is satisfied, if / corresponds to an element of Vj; and to an element 
of Wes (hence to an element of Vs Ws), that is if L be an element 
of Ks e 
7. Summarizing we observe: 
If the productaggregate VW has been covered with numbers and 
if the aggregates G of those numbers corresponding to a same element 
of V converge uniformly to their limits Lg (as regards the covering 
of the positive numbers by the parts of W), the aggregates H of the 
numbers corresponding to a same element of W having the limits 
Li (as regards the covering by the parts of V), then the aggregate 
of the numbers La (as regards the covering by the parts of V) has 
a limit, which is at the same time the limit of the numbers Ly (as 
regards the covering by the parts of W) and is the limit of the 
whole aggregate of numbers (as regards the covering by the parts 
of VW). 
The equality of the two first-mentioned limits means commutativity 
of two lmittransitions. One of the limittransitions relates to the 
covering by the parts of W, the other to the covering by the parts 
ot 
