  Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces. Let
$(\{f_\alpha\}_{\alpha\in \Omega}, \{\tau_\alpha\}_{\alpha\in \Omega})$ and
$(\{g_\beta\}_{\beta\in \Delta}, \{\omega_\beta\}_{\beta\in \Delta})$ be
continuous p-Schauder frames for a Banach space $\mathcal{X}$. Then for every
$x \in \mathcal{X}\setminus\{0\}$, we show that \begin{align} (1) \quad \quad
\quad \quad \mu(\operatorname{supp}(\theta_f x))^\frac{1}{p}
\nu(\operatorname{supp}(\theta_g x))^\frac{1}{q} \geq
\frac{1}{\displaystyle\sup_{\alpha \in \Omega, \beta \in
\Delta}|f_\alpha(\omega_\beta)|}, \quad \nu(\operatorname{supp}(\theta_g
x))^\frac{1}{p} \mu(\operatorname{supp}(\theta_f x))^\frac{1}{q}\geq
\frac{1}{\displaystyle\sup_{\alpha \in \Omega , \beta \in
\Delta}|g_\beta(\tau_\alpha)|}. \end{align} where \begin{align*} &\theta_f:
\mathcal{X} \ni x \mapsto \theta_fx \in \mathcal{L}^p(\Omega, \mu); \quad
\theta_fx: \Omega \ni \alpha \mapsto (\theta_fx) (\alpha):= f_\alpha (x) \in
\mathbb{K}, &\theta_g: \mathcal{X} \ni x \mapsto \theta_gx \in
\mathcal{L}^p(\Delta, \nu); \quad \theta_gx: \Delta \ni \beta \mapsto
(\theta_gx) (\beta):= g_\beta (x) \in \mathbb{K} \end{align*} and $q$ is the
conjugate index of $p$. We call Inequality (1) as \textbf{Functional Continuous
Uncertainty Principle}. It improves the Functional
Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle
obtained by K. Mahesh Krishna in [arXiv:2304.03324v1 [math.FA], 5 April 2023].
It also answers a question asked by Prof. Philip B. Stark to the author. Based
on Donoho-Elad Sparsity Theorem, we formulate Measure Minimization Conjecture.
