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Lebesgue point
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Area of mathematics
Analysis
Real analysis
Measure theory
Measure density
Lebesgue differentiation theorem
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Words: 25
A point
x
∈
R
n
is a Lebesgue point of a locally
Lebesgue integrable function
f
when
lim
r
↓
0
∣
B
r
(
x
)
∣
1
∫
B
r
(
x
)
∣
f
(
y
)
−
f
(
x
)
∣
d
y
=
0.
(371)
The
Lebesgue differentiation theorem
says that almost every point is a Lebesgue point.
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(8)
Lebesgue differentiation theorem
Measure density
Measure theory
Real analysis
Analysis
Area of mathematics
Mathematics
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Differentiation of an indefinite Lebesgue integral
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