Index
Abel tes t fo r convergenc e o f imprope r
integrals, 3 3
absolutely continuou s function , 7 7
almost everywhere , 6 5
approximation theore m fo r measurabl e
functions, 6 5
Arzela theorem , 2 0
Banach indicatrix , 7 8
Banach-Zarecki theorem , 7 8
Bernstein theorem , 8 7
Bessel's inequality , 8 6
Bonnet for m o f secon d mea n valu e the -
orem, 18
Cantor function , 6 6
Caratheodory condition , 5 7
Cauchy theorem , 3 1
Cesaro mea n o f th e Fourie r series , 8 8
change o f variabl e formula , 15
for Lebesgu e integrals , 7 9
Chebyshev inequality , 4 4
convergence i n measure , 6 8
Dini-Lipschitz tes t fo r convergenc e o f
Fourier series , 8 4
Dirichlet tes t fo r convergenc e o f im -
proper integrals , 3 3
Dirichlet-Jordan tes t fo r convergenc e
of Fourie r series , 8 4
duplication formula , 4 1
Egorov theorem , 6 7
elementary set , 5 2
equi-integrable functions , 7 4
essential supremum , 7 0
essentially bounde d function , 7 0
Euler's bet a function , 4 1
Euler's gamm a function , 3 5
Fatou lemm a fo r Rieman n integrals ,
20
Fatou theorem , 9 0
Fejer kernel , 33 4
Fejer theorem , 8 9
Fejer-Lebesgue theorem , 8 9
first mea n valu e theorem , 9
Fourier coefficients , 8 2
Fourier series , 8 2
Frechet theorem , 6 9
Fresnel's integrals , 3 9
function
Lebesgue measurable , 6 4
of bounde d variation , 10
of negativ e variation , 10
of positiv e variation , 10
simple, 6 5
singular, 8 0
Helly selectio n theorem , 18
Helly theorem , 18
Holder condition , 12
Holder inequality , 4 6
integration b y part s fo r Lebesgu e in -
tegrals an d absolutel y continuou s
functions, 8 0
Jensen inequality , 4 7
for Lebesgu e integral , 7 6
Lebesgue constants , 8 8
355
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