So when we have an open cover of a set X means we have a collection of sets [itex]\{ E_\alpha\}_{\alpha \in I}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

such that [itex] X \subset \bigcup_{\alpha \in I} E_\alpha [/itex].

My question comes from measure theory, on the question of finite [itex]\sigma[/itex] -measures,

The definition I'm readying says [itex]\mu[/itex] is [itex]\sigma [/itex] - finite if there exists sets [itex] E_i \in \mathcal{A}[/itex] for [itex]i = 1,2, ...[/itex] such that [itex]\mu(E_i) < \infty[/itex] for each [itex]i[/itex] and [itex]X = \bigcup_{i=1}^\infty E_i[/itex].

Can I say that μ is σ - finite if there exists an open cover for X such that μ(E_{i})< ∞ for each i? Is my understanding correct?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question on Definition of Cover of a Set

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**