Lecture

Construction of Interior and Exterior Measures

Description

This lecture covers the construction of measures in the context of Hilbert spaces, focusing on positive functionals. It explores extreme cases of o-algebras with measures, such as the Dirac measure. Positive functionals on continuous functions with compact support lead to Borel o-algebras and regular, complete, and locally finite measures. The lecture defines interior and exterior measures, highlighting their properties and relationships. It discusses the concepts of sur-additivity and sub-additivity for these measures, providing proofs and examples. The importance of o-additivity for measures is emphasized, aiming for equality rather than inequality in the context of measure theory.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.