這就是個特殊的 Orlicz space, 日後再補.
LlogL(X):={f是可測函數:∃λ>0,s.t.∫X∣f(x)∣λlog(e+∣f(x)∣λ)dx<1}.L\log L(X) := \left\{ f 是可測函數: \exists \lambda > 0, s.t. \int_X \frac{|f(x)|}{\lambda} \log \left( e + \frac{|f(x)|}{\lambda} \right) dx < 1 \right\}.LlogL(X):={f是可測函數:∃λ>0,s.t.∫Xλ∣f(x)∣log(e+λ∣f(x)∣)dx<1}.
∥f∥LlogL(X):=inf{λ>0:∫X∣f(x)∣λlog(e+∣f(x)∣λ)dx<1}.\Vert f \Vert_{L\log L(X)} := \inf \left\{ \lambda > 0: \int_X \frac{|f(x)|}{\lambda} \log \left( e + \frac{|f(x)|}{\lambda} \right) dx < 1 \right\}.∥f∥LlogL(X):=inf{λ>0:∫Xλ∣f(x)∣log(e+λ∣f(x)∣)dx<1}.
