absolute continuity

The absolute continuity of y implies that its derivative exists almost everywhere.

Of course I went to school with I was little, but it was not possible through adolescence to keep an absolute continuity of things.

To do this, one first finds a condition that is weaker than absolute continuity but is satisfied by any approximately differentiable function.

In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity.

For an equivalent definition in terms of measures see the section Relation between the two notions of absolute continuity.

Thus absolute continuity induces a partial ordering of such equivalence classes.

The relation between the two notions of absolute continuity still holds.

This proves absolute continuity.

Thus the notion of contiguity extends the concept of absolute continuity to the sequences of measures.

The notion of contiguity is closely related to that of absolute continuity.