2 Endollared the LaTeX.

I want to know the following is well-known or not:

Let X be a metric space with Hausdorff dimension \alpha. $\alpha$. Then for any \beta $\beta < \alpha, alpha$, X contains a closed subset whose Hausdorff dimension is \beta.$\beta$.

1

# Question on geometric measure theory

I want to know the following is well-known or not:

Let X be a metric space with Hausdorff dimension \alpha. Then for any \beta < \alpha, X contains a closed subset whose Hausdorff dimension is \beta.