Mathematics. — “Remark on Multiple Integrals.” By Prof. L. E.J. 
BROUWER. 
(Communicated in the meeting of June 28, 1919). 
The object of this communication is to make two remarks in 
conjunction with the first part of my paper: “Polydimensional 
Vectordistributions’') presented at the meeting of May 26, 1906. 
Rak 
I. The proof of the generalisation of Srokes's theorem given l.c. 
pp. 66—70 provides this generalisation not only in the Euclidean 
but also in the following ametrie form: 
Turorem. In the n-dimensional space (a,,...2,) let the (p—1)-tuple 
integral 
fF Het, de (es os En) dte: dee +5 STEEN era) 
be given, where the F’s are continuous and finitely and continuously 
differentiable; consider also the p-tuple integral 
IS fue, (rn de de dea, OM ml) 
where 
Da OF; 
Fee, 4 = = 
ie | Our 
(indicatrie j, a, aeg. indicatrix a, ... dy). 
Then, if the two-sided p-dimensional fragment?) G is bounded by 
the two-sided (p—)-dimensional closed space g, the indicatrices of 
G and g corresponding and both G and g possessing a continuously 
varying plane tangent space, the value of (1) over g is equal to the 
value of (2) over G. 
1) See Vol. IX, pp. 66—78; we take the definitions modified in accordance with 
note') on p. 116 le. I take this opportunity of pointing out that on p. 76 Lc. 
lines 183 and 14 “finite sourceless current system’ should be read instead of 
“system of finite closed currents”’. 
3) Math. Annalen 71, p. 306. 
