How do I stop white leaf fungus on turnip greens?

This is probably either downy mildew or powdery mildew. Both these diseases thrive in wet conditions. The best thing to do is keep the leaves dry, especially at night. There are also several fungicides you can use.

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Fungicides
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Powdery Mildew on Zinnias

Related Resources:
Home Vegetable Garden Fungicides
Home Fungicide Guide
Easy Gardening: Turnip and Mustard Greens