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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