miara Lebesgue'a

On the other hand, has a uniform density with respect to and the Lebesgue measure.

For example, the real numbers with the standard Lebesgue measure are σ-finite but not finite.

The Lebesgue measure also has the property of being σ-finite.

The Lebesgue measure on the real line R is a special case of this.

Note that here is indicated the Lebesgue measure on the real line.

The area of the carpet is zero (in standard Lebesgue measure).

This is a special case of the preceding example, using Lebesgue measure, but described in elementary terms.

In this case, the Lebesgue measure of need not be unity.

Consider the Lebesgue measure on the half line (0, ).

Such distributions are not absolutely continuous with respect to Lebesgue measure.