350 SCIENCE PROGRESS 



W. Sierpinski (Giorn. di Mat. 191 6, 54, 314-34) gives an 

 elementary example of an increasing function which has a zero 

 derivative almost everywhere. 



H. B. Phillips (Amer. Journ. Math. 191 8, 40, 235-41) shows 

 how the algebraic sign can be directly attached to the element 

 of integration of multiple integrals, so that such integrals can 

 be treated in this respect like curvilinear integrals. 



N. Lusin (Ann. di Mat. 191 7, 26, 77-129) extends some 

 theorems on integration due to H. Lebesgue and A. Denjoy. 



R. D. Carmichael (Bull. Amer. Math. Soc. 191 8, 24, 348-55) 

 gives a thorough and useful review of de la Vallee Poussin's 

 recent book on Lebesgue integrals (cf. Science Progress, 1917, 

 12, 9). 



J. F. Ritt (Bull. Amer. Math. Soc. 191 8, 24, 225-7) fills a 

 lacuna in what is known about the differentiability of asymp- 

 totic series ; the responsibility for this lacuna being a failure 

 to distinguish between the real and complex domains in this 

 connection. 



A. Kienast (Proc. Camb. Phil. Soc. 191 8, 19, 129-47) gives 

 extensions of Abel's theorem on a limiting value of power-series, 

 and its converse. 



E. Cotton (Compt. rend. 191 7, 164, 389-92) obtains a relation 

 between the radius of convergence of a power-series and the 

 " characteristic number " (Liapounoff) of a certain real or 

 complex function of n which determines the coefficient a„. 



E. Landau (Archiv der Math. 1916, 25, 173-8) gives a new 

 proof of a theorem of G. H. Hardy on the mean value of 

 a certain integral in the theory of analytic functions, and 

 M. Petrovitch (Compt. rend. 191 7, 164, 716-18, 780-2) gives 

 some arithmetical theorems on Cauchy's integral. 



I. Priwaloff (Bull, de la Soc. Math, de France, 1916, 44, 100-3) 

 proves some theorems on conjugate functions, and G. Valiron 

 (ibid. 103-19) obtains some results on the theory of interpolation 

 for whole functions, which seem, from the account given in 

 Rev. sem. (191 8, 26 [1], 34~S), to be closely connected with the 

 complete solution of the problem published by Jourdain in 1905 

 (Journ. fur Math. 128, 169-210). 



H. Bohr (Gott. Nachr. 1916, 276-91) obtains some results on 

 the sum of the coefficients of a power-series, and G. D. Birkhoff 

 (Compt. rend. 191 7, 164, 942-5) has a paper on a generalisation 

 of Taylor's series, 



