Showing a limited preview of this publication:
Abstract
Let X and Y be separable Banach spaces and E be a subset of X. By a random operator from X into Y we mean a rule Φ that assigns to each element x ∈ X a unique Y - valued random variable Φx. Taking into account many circumstances in which the inputs are also subject to the influence of a random environment there arises the need to define the action of Φ on some random inputs. In this paper, some procedures for extending random mappings will be proposed. Some conditions under which a random mapping can be extended to apply to all X-valued random variables will be presented.
Key words.: Random mappings; random operators; action on random inputs; extension of the domain of a random mapping
Received: 2009-06-15
Published Online: 2010-01-22
Published in Print: 2009-December
© de Gruyter 2009
