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Measure density ( $ρ_{μ, A} (x)$ )

For a measurable set

A \subseteq R^{n}

, its density at

x

with respect to a locally finite measure

μ

is

ρ_{μ, A} (x) = lim_{r ↓ 0} \frac{μ ( A \cap B _{r} ( x ))}{μ ( B _{r} ( x ))}

when this limit exists.

Table of contents 112 4
- Lebesgue differentiation theorem Measure density 62 2
  - Lebesgue point Lebesgue differentiation theorem 25
  - Differentiation of an indefinite Lebesgue integral Lebesgue differentiation theorem 19
- Lebesgue density theorem Measure density 25

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