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[MTH411] Measure \(m(\phi)\) in the measure \(m(E)\) of a set\(E\) is _________
zero

[MTH411] Let K be a bounded closed set contained in the open interval \(I\). Then
\(m(K)=m(I)-m(I-K)\)

[MTH411] Let E be a closed set and let G be a bounded open set. If \(E\subseteq G\), then
\(m(E_{1})> m(E_{2})\)

[MTH411] Let X be an arbitrary set. Then a _____________on X is a family of subsets of X that contains and is closed under complementation, formation of countable unions and formation of countable intersections.
algebra

[MTH411] Let X be any set and let M = P(X), the power set of X. Then M is a _________on X
q – algebra

[MTH411] Let X be an infinite set and let M be the collection of all subsets A of X such that A or Ac is fnite. Then M is  ________ on X
algebra

[MTH411] Let\( E_{1}\) and \(E_{2}\) be two sets. If \(E_{1}\\subseteq  E_{2}\), then
\(m(E_{1})\leq m(E_{2})\)

[MTH411] Let X be any set and let M be the collection of all subsets A of X such that either A or Ac is countable. Then M is__________ on X.
q – algebra

[MTH411] The inner measure m*(K) of a bounded set K is the ________ of the measures of all bounded closed sets contained in the set K.
least upper bound

[MTH411] The outer measure m*(K) of a bounded set K is the__________of the measures of all bounded open sets containing the set K.
greatest lower bound