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Lebesgue integral, 260
Lebesgue measurable, 246
Lebesgue’s theorem, 122
Legendre polynomial, 159
lim inf, lim sup, 51
limit of a function, 84
linear approximation, 99
linear fractional transformations, 315
linear functional, 159
Liouville’s theorem, 351
Lipschitz condition, 183
Littlewood’s three principles, 251
local maximum, 101
local minimum, 101
Lusin’s theorem, 252
matrix norms, 165
maximum modulus theorem, 356
mean-square approximation, 228
mean value theorem, 102, 110
measure, 65
measure zero, 120
metric
discrete, 129
Euclidean, 129
Frechet, 162
taxicab, 131
translation invariant, 162
uniform, 131
metric space, 128
Minkowski’s inequality, 155
Mobius transformation, 323
modes of convergence, 191
modular arithmetic, 26
Monotone bounded sequence, 44
monotone convergence theorem, 266
Morera’s theorem, 353
nested sets theorem, 33, 75, 144
non-Archimedian triangle
inequality, 138
norm, 45, 148
open and closed sets, 63
open ball, 131
open set, 63
operator norm, 168
order axioms, 24
orthogonal decompsition, 151
orthonormal basis, 156
orthonormal list, 156
Ostrowski’s theorem, 141
outer measure, 244
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