Amemiya Norm Equals Orlicz Norm in Musielak–Orlicz Spaces.

Let ( Ω, μ) be a σ-finite measure space and Φ : Ω × [0,∞) → [0,∞] be a Musielak–Orlicz function. Denote by L ^Φ( Ω) the Musielak–Orlicz space generated by Φ. We prove that the Amemiya norm equals the Orlicz norm in L ^Φ( Ω). [ABSTRACT FROM AUTHOR]