regular measure

I said, once, that a medical man sometimes has to use psychology in addition to the regular measures against plague.

In particular every signed regular measure is a 0-current:

The use of regular measures (bars) became commonplace by the end of the 17th century.

Lebesgue measure on the real line, R, is a regular measure.

Regular measure, a measure for which every measurable set is "approximately open" and "approximately closed"

In mathematics, an inner regular measure is one for which the measure of a set can be approximated from within by compact subsets.

The Lebesgue outer measure on R is an example of a Borel regular measure.

Let μ and ν be uniformly distributed Borel regular measures on a separable metric space (X, d).

Any Baire probability measure on any locally compact σ-compact Hausdorff space is a regular measure.

A hypermeasure, large-scale or high-level measure, or measure-group is a metric unit in which, generally, each regular measure is one beat (actually hyperbeat) of a larger meter.

In mathematics, the regularity theorem for Lebesgue measure is a result in measure theory that states that Lebesgue measure on the real line is a regular measure.

The Riesz representation theorem is actually a list of several theorems; one of them identifies the dual space of C(X) with the set of regular measures on X.

An outer measure satisfying only the first of these two requirements is called a Borel measure, while an outer measure satisfying only the second requirement is called a regular measure.

It coincides with m on compact and open sets, and m can be reconstructed from M as the unique inner regular measure that is the same as M on compact sets.

If a tight collection M consists of a single measure μ, then (depending upon the author) μ may either be said to be a tight measure or to be an inner regular measure.

Note: In this article we use the Fraktur (whose shape is somewhat reminiscent of for Borel) to indicate a probability based on a regular measure as opposed to one based on a complete measure.

It can be proved that a Borel Regular measure, although introduced here as an outer measure (only countably subadditive), becomes a full measure (countably additive) if restricted to the Borel sets.

He wrote that the ideal of the Fijian poet is poetry with every verse ending with the same vowell of regular measure, which, in practice is often achieved with poetic license through the use of arbitrary abbreviations or lengthenings, and omission of articles, etc.

The fact that all these methods define the same measure on S follows from an elegant result of Christensen: all these measures are obviously uniformly distributed on S, and any two uniformly distributed Borel regular measures on a separable metric space must be constant (positive) multiples of one another.