Since \(\mathcal{D}(\mathbb{R}^d)\subseteq \mathcal{S}(\mathbb{R}^d)\) we have \(\mathcal{S}'(\mathbb{R}^d)\subseteq \mathcal{D}'(\mathbb{R}^d)\), i.e. every tempered distribution is a distribution .
Since \(\mathcal{D}(\mathbb{R}^d)\subseteq \mathcal{S}(\mathbb{R}^d)\) we have \(\mathcal{S}'(\mathbb{R}^d)\subseteq \mathcal{D}'(\mathbb{R}^d)\), i.e. every tempered distribution is a distribution .