Index 201
Lebesgue integral of a bounded
function, 51
Lebesgue measurable, 180
Lebesgue measurable function, 45
Lebesgue measurable set, 31, 182,
183, 189
Lebesgue measure, 31, 174, 190
Lebesgue outer measure, 175
Lebesgue simple, 42
limit, 145
limit in a normed space, 170
limit point, 158
linear function, 98
linear functional, 96, 106
linearity, 42
Littlewood’s three principles, 34, 72
lower bound, 142
Mean value theorem, 161
measurable function, 44, 45
measurable function (complex), 119
measurable partition, 41
measurable set, 31, 174, 182, 189
measurable subset of T , 126
measurable with respect to a
σ-algebra, 73
measure, 73
measure preserving transformation,
130
Minkowski inequality, 87
modulus, 149, 168
monotone, 146
monotone convergence theorem, 70
monotone decreasing, 146
monotone increasing, 146
monotonicity, 42, 181
movie, 139
natural numbers, 141
non-measurable set, 193
norm, 84, 163, 168
normed linear space, 164
nowhere dense, 39
null set, 28
open interval, 156
open set, 156
orbit, 129
orthogonal projection, 99, 107
orthonormal, 165
orthonormal family, 100, 106
outer measure, 175
parallelogram law, 164, 169
perfect, 39
perpendicular, 95, 168
Poincar´ e recurrence theorem, 133
pointwise, 56
positive definite, 88, 105, 163, 167
power set, 154
Pythagorean theorem, 95, 168
Radon-Nikodym derivative, 76
Radon-Nikodym theorem, 76
range, 143
rational numbers, 141
real numbers, 141
real part, 149
recurrent, 129, 132
regulated function, 9
regulated integral, 11
Riemann integrable, 18
Riemann integral, 18
sequence, 144
set difference, 32, 151
set inverse, 144
Sigma algebra, 29
simple, 42
simple functions, 41
square integrable, 84
square integrable complex
functions, 121
square summable, 148
standard Hermitian form, 167
step function, 5
subadditivity, 174
supremum, 142
surjection, 144
surjective, 143
symmetric difference, 35
translation invariance, 26, 31, 173,
178, 190
triangle inequality, 164, 169
uncountable, 152
uniform continuity, 160
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