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Studies In Probability Theory., Ramanathan Subramaniam Dr.

Doctoral Theses

This thesis consists of four chapters.The inpetus for the work in Chapter 1 comes from the concept of 'conditional atom' introduced by ileveu (191. Here, using conditional atoms we generalize the concept of nenatomicity of measures. (We confine ourselves to probability measures). We obtain generalizations of results on non atomic measures in [1), [3] and of Liapounoff's theorem. The results in Chapter 2 have their origins in a paper by Boylan [7]. To study 'e quiconvergence of martingales' Boylan introduced in [7] a metric on the space of complete sub d-algebras of a probability space. A little later, Never showed …