Meteor Stream Membership Criteria

Criteria for the membership of individual meteors in meteor streams are discussed from the point of view of their mathematical and also physical properties. Discussion is also devoted to the motivation. It is shown that standardly used criteria (mainly D-criterion of Southworth and Hawkins, 1963) have unusual mathematical properties in the sense of a term ``distance'', between points in a phase space, and, physical motivation and realization for the purpose of obtaining their final form is not natural and correct, and, moreover, they lead also to at least surprising astrophysical results. General properties of possible criteria are discussed. A new criterion for the membership in meteor streams is suggested. It is based on probability theory. Finally, a problem of meteor orbit determination for known parent body is discussed.