Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 8, Number 2

#### Publication Date: June 1941

Interval-functions

André Gleyzal; 223-230

The extension of rectangle functions

P. Reichelderfer and L. Ringenberg; 231-242

Khintchine’s problem in metric Diophantine approximation

R. J. Duffin and A. C. Schaeffer; 243-255

Non-alternating and non-separating transformations modulo a family of sets

John W. Odle; 256-268

A new proof of a theorem of Menchoff

Raphaël Salem; 269-272

A topology for semi-modular lattices

L. R. Wilcox; 273-285

The arithmetical theory of Birkhoff lattices

R. P. Dilworth; 286-299

An analogue of Green’s theorem in the calculus of variations

Magnus R. Hestenes; 300-311

A generalization of the Aumann-Carathéodory “Starrheitssatz”

Maurice H. Heins; 312-316

The absolute convergence of trigonometrical series

Raphaël Salem; 317-334

The distribution of the number of summands in the partitions of a positive integer

Paul Erdös and Joseph Lehner; 335-345

Riesz summability methods of order $r$, for $\mathcal{R}(r)<0$

G. E. Forsythe; 346-349

Unstable minimal surfaces of higher topological structure

Marston Morse and C. Tompkins; 350-375

The best polynomial approximation of functions possessing derivatives

J. Shohat; 376-385

The decomposition of measures

Paul R. Halmos; 386-392

Functions having subharmonic logarithms

E. F. Beckenbach; 393-400

Riemannian manifolds with positive mean curvature

S. B. Myers; 401-404

An analogue of the Bernoulli polynomials

L. Carlitz; 405-412