Math 156

Measurement

CC-BY- Krauss

The Whole Measure is the Sum of its Parts

First is Heads

1/2 of the total proportion

First tails then Heads

1/4 of the total proportion

Heads in first or second flip

= First Heads or First Tails then Heads

1/2 + 1/4 of the total proportion

Heads in first flip or Tails in Second Flip

1/2 + 1/2 is not correct! NOT DISJOINT

\(\mu:\{A\subset \Omega\}\to [-\infty,\infty]^?\), i.e. maybe some subsets are not measurable.
\(\mu(\emptyset)=0\)
If \(A\) has measurement then \(\mu(\Omega-A\)\) has measurement.
If \(A_1, A_2,\ldots\) disjoint then \(\mu(A_1\sqcup A_2\sqcup \cdot )=\mu(A_1)+\mu(A_2)+\cdots\)

By James Wilson