Measure theory was developed in the late 19th and early 20th centuries.

These separate definitions can be more closely related in terms of measure theory.

One very general version in measure theory is the following :

This paradoxical result is explained by measure theory as follows.

His covering theorem is a fundamental result in measure theory.

The existence and regularity problems are part of geometric measure theory.

He did research in topology, measure theory, statistics, and a variety of other fields.

In particular, is always finite, in contrast with more general measure theory.

Varifolds are the topic of study in geometric measure theory.

In general, it is a result in measure theory.

(although in measure theory, this is often defined as )

More generally, in measure theory and probability theory, either sort of mean plays an important role.

Sometimes, the following constraint is added in the measure theory context:

Probability theory became measure theory with its own problems and terminology.

These set families have applications in measure theory.

It forms a fundamental part of the field of geometric measure theory.

Measure theory is developed from a functional analytic perspective.

Federer wrote more than thirty research papers in addition to his book Geometric measure theory.

In measure theory, proved two more general forms of the ham sandwich theorem.

Some basic results in geometric measure theory can turn out to have surprisingly far-reaching consequences.

More generally, both versions of the principle can be put under the common umbrella of measure theory.

In measure theory, a ring of sets is instead a family closed under unions and set-theoretic differences.

This is conceptually similar to the almost everywhere concept of measure theory, but is not the same.

His research areas were broad, including harmonic analysis, measure theory and algebraic geometry.

Thus in the language of measure theory, almost all n-by-n matrices are invertible.