A collection of measurable sets follows a $\sigma$ algebra.
All sets of measure $0$ is measurable.
My questions are:
What's the significance of sets of measure $0$ in the $\sigma$ algebra of measurable sets? Are they some sort of "identity"?
What's the significance of the proposition:"the translate of a measurable set is measurable." in the set of measurable set's $\sigma$ algebra? Does it somehow suggest an equivelence relation?
Does the previous proposition and sets of measure $0$ carry any interesting effect?