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Studies In Probability Theory., Ramanathan Subramaniam Dr.
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 …
Studies In The Theory Of Measurable Maltifunctions., Sheshi Mohan Srivastava Dr.
Studies In The Theory Of Measurable Maltifunctions., Sheshi Mohan Srivastava Dr.
Doctoral Theses
During the last fifteen years a large number of papers have been devoted to the study of elosed set valued multifunetions. The studies were notivated by both the theoretical and spplica- tional interests that such multifunetions have. From the appli- cational point of view it is worth noting that such multifune- tions arise in varlous problems of control theory, dynanie progra- aning etc. The theoretieal'aspects of these studies belong properly to classieal deseriptive set theory. Classionl deserip- tive set theory asks que stions about how sets are constructed and about other definability properties of sets. The results on closed set …
Invariant Subspaces Of Vector Valued Function Spaces On Bohr Groups., Somesh Chandra Bagchi Dr.
Invariant Subspaces Of Vector Valued Function Spaces On Bohr Groups., Somesh Chandra Bagchi Dr.
Doctoral Theses
The theory of invariant subspaces of various Cunclion-spaces of complox-valued and vector-valued functions on the circle group 13 well known through the 'Loctures on Invariant Subspaces' by Helson ([4]), Replacin; Line circle croup by a Bohr group B (that is, a compact ahelian group whose dual is a subgroup of tho ronl. line R, dense in the topology of R), Helson and Lowdenalager initiated the study of invariant subspaces of L2,(B) in (6]. They discovered that after suitable normalisation, the simply invariant subspaces of L2(B) arcinonc-to-one correspondence with a certain class of functions on R x B, which are called …