# Appendix To Limits For Partial Maxima Of Gaussian Random Vectors

## TL;DR

This paper provides a proof of sample path continuity for Gaussian measures on Banach spaces and explores spectral perturbation results for compact self-adjoint operators on Hilbert spaces.

## Contribution

It offers a short proof for path continuity of Gaussian measures and new results on spectral perturbations of compact operators.

## Key findings

- Proof of sample path continuity for Gaussian measures
- Spectral perturbation results for compact self-adjoint operators
- Applications to Gaussian processes and operator theory

## Abstract

This appendix provides a short proof for sample path continuity of the Brownian motion induced by an arbitrary centered Gaussian measure on a separable Banach space, and also some perturbation results for the spectrum of compact self-adjoint operators on a Hilbert space.