Nonstandard Analysis

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Springer Science & Business Media, 2007 - Mathematics - 252 pages
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This book introduces Robinson's nonstandard analysis, an application of model theory in analysis. Unlike some texts, it does not attempt to teach elementary calculus on the basis of nonstandard analysis, but points to some applications in more advanced analysis. The contents proceed from a discussion of the preliminaries to Nonstandard Models; Nonstandard Real Analysis; Enlargements and Saturated Models; Functionals, Generalized Limits, and Additive Measures; and finally Nonstandard Topology and Functional Analysis. No background in model theory is required, although some familiarity with analysis, topology, or functional analysis is useful. This self-contained book can be understood after a basic calculus course.
  

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Contents

II
1
III
4
IV
13
VI
17
VII
19
VIII
22
IX
34
X
40
XXV
115
XXVI
122
XXVII
125
XXVIII
129
XXIX
140
XXX
148
XXXI
150
XXXII
154

XI
44
XIII
48
XIV
51
XV
59
XVI
70
XVII
74
XVIII
85
XX
90
XXI
92
XXII
103
XXIII
113
XXIV
114
XXXIII
167
XXXIV
170
XXXV
178
XXXVI
185
XXXVII
197
XXXVIII
205
XXXIX
211
XL
216
XLI
241
XLII
245
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