| Summary: | 博士 === 國立清華大學 === 數學系 === 85 === We cosider some limit problems of random elements in this paper.
In Chppter 1,we give the basic definitions and elementry
properties of random elements. And we introduce a space of type
p and the Levy''s inequalities in Banach spaces. In Chapter 2,
we consider the necessary and sufficent conditions of complete
convergence of arrayes of random elements. In Section 2.2, we
obtain the sufficent condions of polynamial order. In Section
2.3, the necessary result is proved. In Section 2.4, we consider
the general cases. In Chapter 3, we consider the almost sure
convergence of weighted sums, using the Marcinkiewicz''s law of
large numbers in a space of type p. In Section 3.2, we develop a
tool-the Marcinkiewicz''s law of large numbers in a space of type
p. In Section 3.3, we discuss the almost sure convergence of
weighted sums of a sequence of random elements, and the weight
is an array of random variables.
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