Equidistributed Sequence - Sequences Equidistributed With Respect To An Arbitrary Measure

Sequences Equidistributed With Respect To An Arbitrary Measure

For an arbitrary probability measure space, a sequence of points is said to be equidistributed with respect to if the mean of point measures converges weakly to :

It is true, for example. that for any probabilistic borel measure on a separable, metrizable space, there exists an equidistributed sequence (with respect to the measure).

Read more about this topic:  Equidistributed Sequence

Famous quotes containing the words respect, arbitrary and/or measure:

    You may, or may not, have better child care instincts than your husband; but his can certainly be developed. If you don’t respect the natural parenting talents that each of you has, you may inadvertently cast the two of you into the skewed but complementary roles of the Expert and the Dumb Apprentice.
    Jean Marzollo (20th century)

    The lore of our fathers is a fabric of sentences. In our hands it develops and changes, through more or less arbitrary and deliberate revisions and additions of our own, more or less directly occasioned by the continuing stimulation of our sense organs. It is a pale gray lore, black with fact and white with convention. But I have found no substantial reasons for concluding that there are any quite black threads in it, or any white ones.
    Willard Van Orman Quine (b. 1908)

    The gifts he gave were that some would be apostles, some prophets, some evangelists, some pastors and teachers, to equip the saints for the work of ministry, for building up the body of Christ, until all of us come to the unity of the faith and of the knowledge of the Son of God, to maturity, to the measure of the full stature of Christ.
    Bible: New Testament, Ephesians 4:11.