On Uniform Convergence Page: 1
iii, 47 leavesView a full description of this thesis.
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CHAPTER I
INTRODUCTION
§1. Preliminary R^marM
1.1. Infinite series were first employed in th^ sevens
teenth eent^ry but little thought waa given them. &eoe#rsdBg
eonverg^mee or divergence* It was generally held, f#r examgtl#
by i^grange^ that if the nth taym of a aeriea appy^aehed
gero M a iB$reaa$4,. the aeries wa$ convergent aven though
Bernoulli had given an exa^le whiah disproved thia. The
first aathasatteiaa to give & noeesa&py and sufficient con-
dition for eonvergenee was Belsan^# but ainee his woyk re*
rained almost ^mknewn for a long period of tist#^ our modern,
theerie# of eonvergenee have come from the work of 3auehy
and Abel.
1
1*2. By an infinite aeQuenee ef real ntnsMrs, in no^
tatien ^a^?* ^ ^ ordered, set of nu^ers which may be
mated biunuqnely with the sat of positive integers and vhieh
are ordered like the natural order of the set of positive
integers, i.e.,
&!#. &2* ^3* *** ^ ^n* *** *
gueh that each value of n# n ^ 1? 2, 3# #** * determines &
3-E. W. Heha-on^ The Theory of y^mstiena ef a Heal Variable!
Vol. II, second edition revised, pp. 5-6.
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Drew, Dan Dale. On Uniform Convergence, thesis, February 1951; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc96930/m1/4/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .