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Unformatted text preview: ents has other intuitively reasonable properties,
and we list some of them below. We number these properties starting at 4, because the list is a
continuation of the three axioms, but we use the lower case letter “e” to label them, reserving the
upper case letter “E” for the axioms.2
Property e.4 The empty set, ∅, is an event (i.e. ∅ ∈ Ω). That is because Ω is an event by Axiom
E.1, so Ωc is an event by Axiom E.2. But Ωc = ∅, so ∅ is an event.
Property e.5 If A and B are events, then AB is an event. To see this, start with De Morgan’s
law: AB = (Ac ∪ B c )c . By Axiom E.2, Ac and B c are events. So by Axiom E.3, Ac ∪ B c is
an event. So by Axiom E.2 a second time, (Ac ∪ B c )c is an event, which is just AB.
Property e.6 More generally, if B1 , B2 , . . . is a list of events then the intersection of all of these
events (the set of outcomes in all of them) B1 B2 · · · is also an event. This is true by the same
reason given for Property e.5, starting with the fact B1 B2 · · · = (B1 ∪...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
- Spring '08
- The Land