Isomorphism of Measure Spaces: Difference between revisions

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===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
Let <math> U </math> be an open set of


: </math> f\colon \mathbb{R}^n \rightarrow \mathbb{R}^m</math>
: <math> f\colon \mathbb{R}^n \rightarrow \mathbb{R}^m</math>


===Mini-Sards Theorem===
===Mini-Sards Theorem===


==Example==
==Example==

Revision as of 07:53, 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

Mini-Sards Theorem

Example