# Are these conditions sufficient for the process to be continuous?

The text book I’m working on considers the following SDE: $$dX(t) = \mu(t)dt + \sigma(t)dW(t)$$, where $$\mu$$ is defined to be a càdlàg predictable and finite variation process, while $$\sigma$$ is a square integrable, predictable, non-decreasing process. Then it rules out the possibility of any jump in the process $$X$$. Is it correct to conclude that the process $$\mu$$ is continuous and hence has finite quadratic variation?