MTH411
1. If the bounded open set G is the union of finite or denumerable family of pairwise disjoint open sets then \(\hspace{1.0cm}\).
\(m(G) = 0\)
\(m(G) = \sum_{k} m(G_k )\)
\(m(G) < \sum_{k} m(G_k )\)
\(m(G) > \sum_{k} m(G_k )\)
2. If a finite number of pairwise disjoint open intervals \(I_l, I_2, I_3 , \ldots I_n\) are contained in an open interval G, then \(\hspace{1.0cm}\).
\(m(G) < \sum_{k=1}^{n} m(I_k )\)
\(m(G) \leq\sum_{k=1}^{n} m(I_k )\)
\(m(G) \geq\sum_{k=1}^{n} m(I_k )\)
m(G) = \(0\)
3. \(m(E_1 \cup E_2) = m(E_1) + m(E_2)\) for \(E_1 \cap E_2 = \) \(\hspace{1.0cm}\).
\(0\)
\(\emptyset\)
\(\infty\)
1
4. The concept of measure m(E) of a set E is a generalization of measuring the \(\hspace{1.0cm}\) of a line segment.
length
points
areas
volume
5. The measure m(G) of a non empty bounded open set G is the sum of the \(\hspace{1.0cm}\) of all its component intervals.
length
points
areas
volume
6. m(E + x) = m(E), where E + x means the \(\hspace{1.0cm}\) of E distance x.
dilation
rotation
transformation
translation
7. Let \((X, M_X)\) and \((Y, M_Y)\) be measurable spaces. If E is a subset of \(X \times Y\) that belongs to \(M_{X} \times M_{Y}\) then each section \(E_y\) belongs to \(\hspace{1.0cm}\).
\(\M_{X \times Y}\)
\(\M_y\)
\(\M_{X \times Y}\)
\(\M_x\)
8. The measure of a bounded open set G is the \(\hspace{1.0cm}\) of the measures of all bounded open sets containing G.
sum
greatest lower bound
least upper bound
upper bound
9. Let the open interval J be the union of finite or denumerable family of open sets (that is, \(J = \cup_k G_k )\). Then \(\hspace{1.0cm}\).
\(m(J) \leq \sum_{k} m(G_k )\)
\(m(J) \geq\sum_{k} m(G_k )\)
\(m(J) = \sum_{k} m(G_k )\)
\(m(J) > \sum_{k} m(G_k )\)
10. The concept of measure m(E) of a set E is a generalization of measuring the \(\hspace{1.0cm}\) of a space.
length
points
areas
volume
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