Isomorphism of Measure Spaces: Difference between revisions
Jump to navigation
Jump to search
| Line 15: | Line 15: | ||
===Smooth maps send sets of measure zero to sets of measure zero=== | ===Smooth maps send sets of measure zero to sets of measure zero=== | ||
Let <math> U </math> be an open set of <math> \mathbb{R}^n</math>, and let | Let <math> U </math> be an open set of <math> \mathbb{R}^n</math>, and let <math> f\colon U \rightarrow \mathbb{R}^m</math> be a smooth map. | ||
If <math> A\subset U</math> is of measure zero, then <math> f(A)</math> is of measure zero. | |||
===Mini-Sards Theorem=== | ===Mini-Sards Theorem=== | ||
==Example== | ==Example== | ||
Revision as of 07:57, 18 December 2020
Motivation
Definition
Basic Theorem
Properties
Smooth maps send sets of measure zero to sets of measure zero
Let be an open set of , and let be a smooth map. If is of measure zero, then is of measure zero.
