Why Are Separable Metric Spaces Essential for Random Operators?

[adnan jahan]

operators are those functions which are having domain any set or any function the range is also a function. In simple words operators is a machine which is having domain and range as a set of functions. random operators are those spectiol type of fuctions which are define on a measured space.

 

[adnan jahan]

My question is ,
1- why in the case of random operators we do use separable metric space ?
2- random operator is an operator must have domain as a set of functions but in some cases we took elements of any sets as the member of its domain what is basically reason for that