SOME REMARKS ON SET THEORY, IX. COMBINATORIAL
... where m(F(n)) > u > 0 for n E S . Clearly, m(G t ) > u and Gt+l C G t (t = 1, 2, . . .) (throughout the paper, the symbol C refers to inclusion in the broad sense) . Thus, by a classical theorem of Lebesgue, m(G) > u . Since each c in G is contained in infinitely many sets F(t), this completes the p ...
... where m(F(n)) > u > 0 for n E S . Clearly, m(G t ) > u and Gt+l C G t (t = 1, 2, . . .) (throughout the paper, the symbol C refers to inclusion in the broad sense) . Thus, by a classical theorem of Lebesgue, m(G) > u . Since each c in G is contained in infinitely many sets F(t), this completes the p ...
A PROBABILISTIC INTERPRETATION OF A SEQUENCE RELATED
... expressed in terms of the classical Gegenbauer polynomials C n 2 . The coefficients a n are also generalized to a family of numbers {a n (µ)} with parameter µ. The special cases µ = 0 and µ = ± 12 are discussed in detail. Section 2 produces a recurrence for {a n } from which the facts that a n is in ...
... expressed in terms of the classical Gegenbauer polynomials C n 2 . The coefficients a n are also generalized to a family of numbers {a n (µ)} with parameter µ. The special cases µ = 0 and µ = ± 12 are discussed in detail. Section 2 produces a recurrence for {a n } from which the facts that a n is in ...
