No-Lose Theorem for Higgs Boson Searches at a Future Linear Collider

Assuming perturbativity up to a high energy scale ~10¹⁶GeV, we demonstrate that a future e⁺e^- linear collider operating at √s0ex0ex=0ex0ex500GeV with ∫L0ex0ex=0ex0ex500fb^-1 per year (such as the recently proposed TESLA facility) will detect a Higgs boson signal regardless of the complexity of the Higgs sector and of how the Higgs bosons decay.