Recent content by Cascabel

  1. C

    Graduate Measure theory question: Countable sub-additivity

    Sorry, figured it out. Sorry, figured it out, ##m^* \left (\bigcup_{j=0}^{\infty}E_j \right ) \neq \sum_{j=0}^{\infty} m^*(E_j)##.
  2. C

    Graduate Measure theory question: Countable sub-additivity

    I have a question on sub-additivity. For sets ##E## and ##E_j##, the property states that if ##E=\bigcup_{j=0}^{\infty}E_j## then ##m^*(E) \leq \sum_{j=0}^{\infty}m^*(E_j)##, where ##m^*(x)## is the external measure of ##x##. Since ##E\subset \bigcup_{j=0}^{\infty}E_j##, by set...