Index
A0*, one-sided bipolar of set A, 135, 249
A*, one-sided polar of set A, 134, 249
AfF, vector space of afRne functions, 227
A°, polar of set A, 248
A°°, bipolar of set A, 249
Ax, half-ray generated by x, 37, 40
absolute polar of a set, 248
absolute value
of functional, 56
of operator, 54
of vector, 14
absorbing set, 33, 110, 244
additive function, 23, 184
additive mapping, 23, 184
adjoint operator, 148
Hilbert space, 109
affine function, 221, 227
afRne transformation, 231
Alaoglu-Bourbaki theorem, 248
algebraic dual, 205, 246
algebraic dual of a vector space, 31, 246
algebraic separating hyperplane theorem,
251
almost Archimedean cone, 12
almost Archimedean ordered vector space,
12
alternative
concave, 150
Farkas, 149
operator, 148
Stiemke, 149
wedge, 148
Ando's theorem, 66, 88, 91, 92
angle of an ice cream cone, 99
antisymmetry, 3
Archimedean cone, 11, 63, 119, 128
Archimedean ordered vector space, 11
Archimedean property, 11
arrangement generated by afRne functions,
235
arrangement of hyperplanes, 234
associative law, 178
atom, 39
axis of ice cream cone, 99
/3(L, Z/), strong topology on L, 251
/3(Z/,L), strong topology on L', 251
A°°, bipolar of set A, 249
[£], full hull of set B, 6
balanced set, 6, 244
Banach lattice, 85
Banach space, 253
ordered, 85
reflexive, 254
separable, 254
with the Levi property, 89
with the strong Levi property, 89
Banach-Steinhaus theorem, 254
base of cone, 39
pseudo, 200
basis
Hamel, 124
positive, 125
Yudin, 125
bilinear mapping, 247
bilinearity of a dual pair, 247
bipolar of a set, 249
bipolar theorem, 249
one-sided, 135, 249
Birkhoff's identity, 21
Birkhoff's inequalities, 21
Borel sets, 75
271
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