- #1

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## Homework Statement

I'm new to Measure Theory, and to be honest, I'm having a really hard time making any sense of it at all. My prof is a nice guy, but his approach to teaching involves giving zero worked solutions. This doesn't work for me. Personally I need to see solutions to get an idea of how to work these problems out, and get an idea of what everything means.

I have a number of problems where I've been asked to find the smallest σ-algebras of subsets of ℝ where f:ℝ→ℝ is a measurable function. The first question is given below:

## Homework Equations

f(x) = -1 if x <= 0, and f(x) = 1 if x > 0

## The Attempt at a Solution

Don't laugh - as I said I really don't know what I'm doing here...

I can see that sub-intervals of X = ℝ: (-∞, 0) and [0, ∞) are in one-to-one correspondence with the singleton set 2 = {-1,1}. So there are |P(2)| = 2^2=4 sets in the σ-algebra.

Would the answer be: {∅,(-∞,0),[0,∞),ℝ} ?

Am I even close to being on the right track here?