@article{das_2021, 
  title={Epsilon multiplicity for Noetherian graded algebras}, 
  abstractNote={The notion of epsilon multiplicity was originally defined by Ulrich and
Validashti as a limsup and they used it to detect integral dependence of
modules. It is important to know if it can be realized as a limit. In this
article we show that the relative epsilon multiplicity of reduced Noetherian
graded algebras over an excellent local ring exists as a limit. An important
special case of a result of Cutkosky concerning epsilon multiplicity, is
obtained as a corollary of our main theorem. We also develop the notion of
mixed epsilon multiplicity for monomial ideals.}, 
  author={Das}, 
  year={2021}, 
  month={Sep}
  }