Abstracts of Miscellaneous Theses for Higher Degrees |
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a₁ a₁a a₂ a₂a b₁ b₂ Banach and Tarski bounded elements bounded equivalent elements Bryn Mawr College congruence corresponding elements corresponding o-elements defined DEFINITION denote disjoint base elements disjoint elements DOROTHY MAHARAM dyadic expansions element of I(a equal measure equivalence relation euclidean space exists a sequence exists an element field of sets finite set finite sums Haar measure holds infimum infinite isomorphism of Þ lattice Lebesgue measurable LEMMA limits of monotonic maximum integer measure function measure-preserving transformation measure-values modulo the null monotonic sequences multiplicative constant necessary and sufficient nested sequence null sets o-isomorphism P-equivalence pair partial ordering positive numbers principal ideals regular basis residue class ring respective limits sequence of disjoint sequence of elements sequences of bounded set of elements set of positive Sk,r Sk,T sponding sufficient condition sum of disjoint Suppose supremum theorem of Banach unbounded unique