query: If $m < n$ then $\mathbb{R}^m \subset \mathbb{R}^n$ have null measure
positive_passages.docid: 153747
positive_passages.text: Sub-dimensional linear subspaces of $\mathbb{R}^{n}$ have measure zero.
negative_passages.docid: 19452
negative_passages.text: Restriction of a Lebesgue integral to a subset of a measurable set.
negative_passages.docid: 134310
negative_passages.text: Minkowski sum of a positive Lebesgue measure set and $\mathbb{Q}$.
negative_passages.docid: 44069
negative_passages.text: Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
negative_passages.docid: 69398
negative_passages.text: Rank-nullity theorem for free $\mathbb Z$-modules
negative_passages.docid: 80735
negative_passages.text: Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
negative_passages.docid: 67259
negative_passages.text: Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
negative_passages.docid: 3023
negative_passages.text: Construction of a Borel set with positive but not full measure in each interval
negative_passages.docid: 59804
negative_passages.text: Show that the plane $\{su+tv|s,t \in\Bbb R\}$ in $\Bbb R^3$ is equal to the null space of some element of $(\Bbb R^3)^{*}$.
negative_passages.docid: 22558
negative_passages.text: Vitali-type set with given outer measure
negative_passages.docid: 55864
negative_passages.text: Is there a null sequence that is in not in $\ell_p$ for any $p<\infty$?
negative_passages.docid: 107160
negative_passages.text: Open Set and Measure Theory
negative_passages.docid: 88602
negative_passages.text: Inner regularity of Lebesgue measurable sets
negative_passages.docid: 66272
negative_passages.text: Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
negative_passages.docid: 47187
negative_passages.text: Proving the measure of an increasing sequence of measurable sets is the limit of the measures
negative_passages.docid: 74330
negative_passages.text: $\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
negative_passages.docid: 153551
negative_passages.text: Is the null set a subset of every set?