Almost everywhere convergence for sequences of continuous functions
Authors:
K. Schrader and S. Umamaheswaram
Journal:
Proc. Amer. Math. Soc. 47 (1975), 387392
MSC:
Primary 40A05
MathSciNet review:
0352773
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: The main result in this paper is the following theorem. Theorem 1.1. Let , be a sequence of continuous real valued functions defined on the bounded interval . Let , where each is a relatively open subinterval of and for . Assume there exists a function , such that is a nondecreasing function of and for all sufficiently large, where is Lebesgue measure and . Then contains a subsequence which converges almost everywhere to a Lebesgue measurable function .
 [1]
F. Ramsey, On a problem of formal logic, Proc. London Math. Soc. (2) 30 (1930), 264286.
 [2]
, The foundations of mathematics, HarcourtBrace, New York, 1931.
 [3]
Keith
Schrader, A generalization of the Helly
selection theorem, Bull. Amer. Math. Soc.
78 (1972),
415–419. MR 0299740
(45 #8788), http://dx.doi.org/10.1090/S000299041972129239
 [4]
K.
Schrader, A pointwise convergence theorem for
sequences of continuous functions., Trans.
Amer. Math. Soc. 159 (1971), 155–163. MR 0280902
(43 #6621), http://dx.doi.org/10.1090/S00029947197102809026
 [1]
 F. Ramsey, On a problem of formal logic, Proc. London Math. Soc. (2) 30 (1930), 264286.
 [2]
 , The foundations of mathematics, HarcourtBrace, New York, 1931.
 [3]
 K. Schrader, A generalization of the Helly selection theorem, Bull. Amer. Math. Soc. 78 (1972), 415419. MR 45 #8788. MR 0299740 (45:8788)
 [4]
 , A pointwise convergence theorem for sequences of continuous functions, Trans. Amer. Math. Soc. 159 (1971), 155163. MR 43 #6621. MR 0280902 (43:6621)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC:
40A05
Retrieve articles in all journals
with MSC:
40A05
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919750352773X
PII:
S 00029939(1975)0352773X
Keywords:
Sequences of functions,
convergent subsequences,
almost everywhere convergence
Article copyright:
© Copyright 1975
American Mathematical Society
