TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

EDITED BY

A. A. ALBERT OSCAR ZARISKI ANTONI ZYGMUND

WITH THE COOPERATION OF

RICHARD BRAUER NELSON DUNFORD WILLIAM FELLER G. A. HEDLUND NATHAN JACOBSON IRVING KAPLANSKY S. C. KLEENE M. S. KNEBELMAN SAUNDERS MacLANE C. B. MORREY W. T. REID O. F. G. SCHILLING N. E. STEENROD J. J. STOKER D. J. STRUIK HASSLER WHITNEY R. L. WILDER

VOLUME 62 JULY TO DECEMBER 1947

PUBLISHED BY THE SOCIETY MENASHA, WIS., AND NEW YORK 1947

Reprinted with the permission of The American Mathematical Society

Johnson Reprint Corporation Johnson Reprint Company Limited 111 Fifth Avenue, New York, N. Y. 10003 Berkeley Square House, London, W. 1 First reprinting, 1964, Johnson Reprint Corporation

PRINTED IN THE UNITED STATES OF AMERICA TABLE OF CONTENTS VOLUME 62, JULY TO DECEMBER, 1947

Arens, R. F., and Kelley, J. L. Characterizations of the space of con- tinuous functions over a compact Hausdorff space. 499 Baer, R. Direct decompositions. 62 Bellman, R. On the boundedness of solutions of nonlinear differential and difference equations. 357 Bergman, S. Two-dimensional subsonic flows of a compressible fluid and their singularities. 452 Blumenthal, L. M. Congruence and superposability in elliptic space.. 431

Chang, S. C. Errata for Contributions to projective theory of singular points of space curves. 548 Day, M. M. Polygons circumscribed about closed convex curves. 315 Day, M. M. Some characterizations of inner-product spaces. 320 Dushnik, B. Maximal sums of ordinals. 240 Eilenberg, S. Errata for Homology of spaces with operators. 1. 548

Erdös, P., and Fried, H. On the connection between gaps in power series and the roots of their partial sums. 53 Fédérer, H. The (p, k) rectifiable subsets of n space. 114 Fédérer, H. Dimension and measure. 536

Frank, E. On the real parts of the zeros of complex polynomials and applications to continued fraction expansions of analytic functions.. 272

Fried, H., and Erdös, P. On the connection between gaps in power series and the roots of their partial sums. 53 Hestenes, M. R. An indirect sufficiency proof for the problem of Bolza in nonparametric form. 509

Johnson, R. E., and Kiokemeister, F. The endomorphisms of the total operator domain of an infinite module. 404

Kalisch, G. K. Errata for On special Jordan algebras. 548 Kaplan, S. Homology properties of arbitrary subsets of Euclidean spaces. 248 Kelley, J. L., and Arens, R. F. Characterizations of the space of con- tinuous functions over a compact Hausdorff space. 499

Kiokemeister, F., and Johnson, R. E. The endomorphisms of the total operator domain of an infinite module. 404

Lonseth, A. T. The propagation of error in linear problems. 193 MacLane, G. R. Concerning the uniformization of certain Riemann surfaces allied to the inverse-cosine and inverse-gamma surfaces... 99 Pollard, H. The mean convergence of orthogonal series. 1. 387 Reichelderfer, P. V. On the definition of the essential multiplicity for continuous transformations in the plane. 284 Shen, Y. C. Interpolation to some classes of analytic functions by func- tions with pre-assigned poles. 338 SzÁsz, O. On Möbius' inversion formula and closed sets of functions.. 213

Zariski, O. The concept of a simple point of an abstract algebraic variety. 1