Abstract Measure Page: 2
iii, 44 leavesView a full description of this thesis.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
K H M a rin£ of se$t* then JH® gqipty igt J2
i£ la B.
Proof. If 1 is a set of a* then by (Z) of 1.32,
A • A f E.
1.3. Lemma. J£ A 6 a B € R# then A f\ B € 1.
Proof. An B - A ~ (A - 3)*
Learna. Tfa® Intersection of any collection
£4m§ M slit & £4a&*
Proof. Let R to® the intersection ©f the collection ©f
rings. If A e R and B f R, then A and B are contained in
every ring of the collection. It follows that A u b e H
and A - B € R.
1.5. Theorem, T la a class of sets, then there
®3ritst3 & unique ring R(T) such that R(T) o T and such that
J£ R It *BZ fitter rlnS f $3to RCH <=
Proof. The class of all subsets of X is a ring, so at
least one ring containing T exists. Let B(T) be the inter-
section ©f all rings defined on X and containing T. R(T)
is a ring by 1 4# It is ©brious that R(T) Is the smallest
ring which contains T.
R(T) will be designated as the ring generated by the
class of sets T.
1.6. Theorem. If T is a class of sets, then the class R
o£ sets such that each set of 1 ca& bg. cohered M. ft. finite
union of sets ill £*££♦ £B& * ^ R(T) cs R.
Proof. If A £ R and B « R, then
Upcoming Pages
Here’s what’s next.
Search Inside
This thesis can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Thesis.
Bridges, Robert Miller. Abstract Measure, thesis, 1957; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc107950/m1/5/: accessed May 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .