Regarding the completeness of a metric space and measure space, are they related in any way or is completeness just another term being used in different fields of mathematics?
The definition for both completeness I know is as follows:
Metric space: A metric space $(X,d)$ is complete if every Cauchy sequence of $X$ converges
Measure space: A measure space $(X,\mathscr{A},\mu)$ is called complete if for every null set $A \in \mathscr{A}$, every $E \subseteq A$ is also in $\mathscr{A}$ i.e. $\mathscr{A}$ contains every subset of a null set.
