# Example showing L1 is not a reflexive space [duplicate]

I know that the $$L^p$$ spaces are reflexive for $$1. I want to explicitly show that $$L^1((0,1),\mathbb{R})$$ is not reflexive by finding an element of $$L^1$$** that is not in $$L^1$$. To be more precise:

There is a canonical embedding $$J: X \rightarrow X^{**}$$ that is given by

$$J(x)(y)=y(x)$$

I want to find an element of $$L^1$$** that doesn't get mapped to by $$J$$.