An integral type characterization of constant functions on metric-measure spaces

作者：Ranjbar Motlagh Alireza^*

来源：Journal of Mathematical Analysis and Applications, 2012, 385(1): 194-201.

DOI：10.1016/j.jmaa.2011.06.020

• Metric-measure spaces
• Doubling condition
• Heat kernel

The main purpose of this article is to generalize a characterization of constant functions to the context of metric-measure spaces. In fact, we approximate a measurable function, in terms of a certain integrability condition, by Lipschitz functions. Then, similar to Brezis (2002) [2], we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be constant a.e. Also, we provide a different proof for the main result of Pietruska-Paluba (2004) [7] in the setting of Dirichlet forms.

• 出版日期2012-1-1