1. Measure of specific set...

Hi I am trying to work out which seems to be an obvious fact but can't see it!

Let A be a set s.t. A = {x: y(x) < k(x)/p}. Then u(A) = measure of A >= (1-p).

Note 0<p<1.

The functions are defined as follows:
y(x) is a random variable
k(x) is the mean of the random variable y(x)

Thank you!

2. Re: Measure of specific set...

I don't know probability, but could you clarify some things:

1. A random variable is a measurable function from a set (measure space) with unit measure to the reals, right?

2. How do you define the mean of the random variable?

This certainly looks more like an analysis problem so if you could use as little terms from probability the better (at least for me).

3. Re: Measure of specific set...

Maybe some more info will help. The random variable is from a distribution with a density function \f_v say. Then the random variable \y(x) has a mean of (or expected value of) \mathbb{E} [\y(x)] = \int_a^b \x \! \f_v \, \mathrm{d}x . I know also that \y(x) \< DB where \D,\B are real numbers.

Why does not latex work?